diff --git a/README.md b/README.md
index 85c81c11..4c00619c 100644
--- a/README.md
+++ b/README.md
@@ -203,6 +203,9 @@ Component documentation:
  * [Error handling](doc/component/Error_handling.markdown)
    * Column information for errors
    * Error recovery (parsing of syntactically incorrect code)
+ * [Constant expression evaluation](component/Constant_expression_evaluation.markdown)
+   * Evaluating constant/property/etc initializers
+   * Handling errors and unsupported expressions
  * [Performance](doc/component/Performance.markdown)
    * Disabling XDebug
    * Reusing objects
diff --git a/doc/README.md b/doc/README.md
index 510b131a..c055f8b9 100644
--- a/doc/README.md
+++ b/doc/README.md
@@ -27,6 +27,9 @@ Component documentation
   * [Error handling](component/Error_handling.markdown)
     * Column information for errors
     * Error recovery (parsing of syntactically incorrect code)
+  * [Constant expression evaluation](component/Constant_expression_evaluation.markdown)
+    * Evaluating constant/property/etc initializers
+    * Handling errors and unsupported expressions
   * [Performance](component/Performance.markdown)
     * Disabling XDebug
     * Reusing objects
diff --git a/doc/component/Constant_expression_evaluation.markdown b/doc/component/Constant_expression_evaluation.markdown
new file mode 100644
index 00000000..9ab4f5c3
--- /dev/null
+++ b/doc/component/Constant_expression_evaluation.markdown
@@ -0,0 +1,115 @@
+Constant expression evaluation
+==============================
+
+Initializers for constants, properties, parameters, etc. have limited support for expressions. For
+example:
+
+```php
+<?php
+class Test {
+    const SECONDS_IN_HOUR = 60 * 60;
+    const SECONDS_IN_DAY = 24 * self::SECONDS_IN_HOUR;
+}
+```
+
+PHP-Parser supports evaluation of such constant expressions through the `ConstExprEvaluator` class:
+
+```php
+<?php
+
+use PhpParser\{ConstExprEvaluator, ConstExprEvaluationException};
+
+$evalutator = new ConstExprEvaluator();
+try {
+    $value = $evalutator->evaluateSilently($someExpr);
+} catch (ConstExprEvaluationException $e) {
+    // Either the expression contains unsupported expression types,
+    // or an error occurred during evaluation
+}
+```
+
+Error handling
+--------------
+
+The constant evaluator provides two methods, `evaluateDirectly()` and `evaluateSilently()`, which
+differ in error behavior. `evaluateDirectly()` will evaluate the expression as PHP would, including
+any generated warnings or Errors. `evaluateSilently()` will instead convert warnings and Errors into
+a `ConstExprEvaluationException`. For example:
+
+```php
+<?php
+
+use PhpParser\{ConstExprEvaluator, ConstExprEvaluationException};
+use PhpParser\Node\{Expr, Scalar};
+
+$evaluator = new ConstExprEvaluator();
+
+// 10 / 0
+$expr = new Expr\BinaryOp\Div(new Scalar\LNumber(10), new Scalar\LNumber(0));
+
+var_dump($evaluator->evaluateDirectly($expr)); // float(INF)
+// Warning: Division by zero
+
+try {
+    $evaluator->evaluateSilently($expr);
+} catch (ConstExprEvaluationException $e) {
+    var_dump($e->getPrevious()->getMessage()); // Division by zero
+}
+```
+
+For the purposes of static analysis, you will likely want to use `evaluateSilently()` and leave
+erroring expressions unevaluated.
+
+Unsupported expressions and evaluator fallback
+----------------------------------------------
+
+The constant expression evaluator supports all expression types that are permitted in constant
+expressions, apart from the following:
+
+ * `Scalar\MagicConst\*`
+ * `Expr\ConstFetch` (only null/false/true are handled)
+ * `Expr\ClassConstFetch`
+
+Handling these expression types requires non-local information, such as which global constants are
+defined. By default, the evaluator will throw a `ConstExprEvaluationException` when it encounters
+an unsupported expression type.
+
+It is possible to override this behavior and support resolution for these expression types by
+specifying an evaluation fallback function:
+
+```php
+<?php
+
+use PhpParser\{ConstExprEvaluator, ConstExprEvaluationException};
+use PhpParser\Node\Expr;
+
+$evalutator = new ConstExprEvaluator(function(Expr $expr) {
+    if ($expr instanceof Expr\ConstFetch) {
+        return fetchConstantSomehow($expr);
+    }
+    if ($expr instanceof Expr\ClassConstFetch) {
+        return fetchClassConstantSomehow($expr);
+    }
+    // etc.
+    throw new ConstExprEvaluationException(
+        "Expression of type {$expr->getType()} cannot be evaluated");
+});
+
+try {
+    $evalutator->evaluateSilently($someExpr);
+} catch (ConstExprEvaluationException $e) {
+    // Handle exception
+}
+```
+
+Implementers are advised to ensure that evaluation of indirect constant references cannot lead to
+infinite recursion. For example, the following code could lead to infinite recursion if constant
+lookup is implemented naively.
+
+```php
+<?php
+class Test {
+    const A = self::B;
+    const B = self::A;
+}
+```
\ No newline at end of file
diff --git a/lib/PhpParser/ConstExprEvaluator.php b/lib/PhpParser/ConstExprEvaluator.php
index 458b69bf..7f02e6f2 100644
--- a/lib/PhpParser/ConstExprEvaluator.php
+++ b/lib/PhpParser/ConstExprEvaluator.php
@@ -20,11 +20,7 @@ use PhpParser\Node\Scalar;
  *
  * The fallback evaluator should throw ConstExprEvaluationException for nodes it cannot evaluate.
  *
- * The evaluation is performed as PHP would perform it, and as such may generate notices, warnings
- * or Errors. For example, if the expression `1%0` is evaluated, an ArithmeticError is thrown. It is
- * left to the consumer to handle these as appropriate.
- *
- * The evaluation is also dependent on runtime configuration in two respects: Firstly, floating
+ * The evaluation is dependent on runtime configuration in two respects: Firstly, floating
  * point to string conversions are affected by the precision ini setting. Secondly, they are also
  * affected by the LC_NUMERIC locale.
  */
@@ -49,7 +45,10 @@ class ConstExprEvaluator
     }
 
     /**
-     * Evaluates a constant expression into a PHP value.
+     * Silently evaluates a constant expression into a PHP value.
+     *
+     * Thrown Errors, warnings or notices will be converted into a ConstExprEvaluationException.
+     * The original source of the exception is available through getPrevious().
      *
      * If some part of the expression cannot be evaluated, the fallback evaluator passed to the
      * constructor will be invoked. By default, if no fallback is provided, an exception of type
@@ -59,9 +58,49 @@ class ConstExprEvaluator
      *
      * @param Expr $expr Constant expression to evaluate
      * @return mixed Result of evaluation
+     *
+     * @throws ConstExprEvaluationException if the expression cannot be evaluated or an error occurred
+     */
+    public function evaluateSilently(Expr $expr) {
+        set_error_handler(function($num, $str, $file, $line) {
+            throw new \ErrorException($str, 0, $num, $file, $line);
+        });
+
+        try {
+            return $this->evaluate($expr);
+        } catch (\Throwable $e) {
+            if (!$e instanceof ConstExprEvaluationException) {
+                $e = new ConstExprEvaluationException(
+                    "An error occurred during constant expression evaluation", 0, $e);
+            }
+            throw $e;
+        } finally {
+            restore_error_handler();
+        }
+    }
+
+    /**
+     * Directly evaluates a constant expression into a PHP value.
+     *
+     * May generate Error exceptions, warnings or notices. Use evaluateSilently() to convert these
+     * into a ConstExprEvaluationException.
+     *
+     * If some part of the expression cannot be evaluated, the fallback evaluator passed to the
+     * constructor will be invoked. By default, if no fallback is provided, an exception of type
+     * ConstExprEvaluationException is thrown.
+     *
+     * See class doc comment for caveats and limitations.
+     *
+     * @param Expr $expr Constant expression to evaluate
+     * @return mixed Result of evaluation
+     *
      * @throws ConstExprEvaluationException if the expression cannot be evaluated
      */
-    public function evaluate(Expr $expr) {
+    public function evaluateDirectly(Expr $expr) {
+        return $this->evaluate($expr);
+    }
+
+    private function evaluate(Expr $expr) {
         if ($expr instanceof Scalar\LNumber
             || $expr instanceof Scalar\DNumber
             || $expr instanceof Scalar\String_
diff --git a/test/PhpParser/ConstExprEvaluatorTest.php b/test/PhpParser/ConstExprEvaluatorTest.php
index 4f6cebd5..d0a83fff 100644
--- a/test/PhpParser/ConstExprEvaluatorTest.php
+++ b/test/PhpParser/ConstExprEvaluatorTest.php
@@ -13,7 +13,7 @@ class ConstExprEvaluatorTest extends TestCase
         $parser = new Parser\Php7(new Lexer());
         $expr = $parser->parse('<?php ' . $exprString . ';')[0]->expr;
         $evaluator = new ConstExprEvaluator();
-        $this->assertSame($expected, $evaluator->evaluate($expr));
+        $this->assertSame($expected, $evaluator->evaluateDirectly($expr));
     }
 
     public function provideTestEvaluate() {
@@ -79,7 +79,7 @@ class ConstExprEvaluatorTest extends TestCase
      */
     public function testEvaluateFails() {
         $evaluator = new ConstExprEvaluator();
-        $evaluator->evaluate(new Expr\Variable('a'));
+        $evaluator->evaluateDirectly(new Expr\Variable('a'));
     }
 
     public function testEvaluateFallback() {
@@ -93,6 +93,41 @@ class ConstExprEvaluatorTest extends TestCase
             new Scalar\LNumber(8),
             new Scalar\MagicConst\Line()
         );
-        $this->assertSame(50, $evaluator->evaluate($expr));
+        $this->assertSame(50, $evaluator->evaluateDirectly($expr));
+    }
+
+    /**
+     * @dataProvider provideTestEvaluateSilently
+     */
+    public function testEvaluateSilently($expr, $exception, $msg) {
+        $evaluator = new ConstExprEvaluator();
+
+        try {
+            $evaluator->evaluateSilently($expr);
+        } catch (ConstExprEvaluationException $e) {
+            $this->assertSame(
+                'An error occurred during constant expression evaluation',
+                $e->getMessage()
+            );
+
+            $prev = $e->getPrevious();
+            $this->assertInstanceOf($exception, $prev);
+            $this->assertSame($msg, $prev->getMessage());
+        }
+    }
+
+    public function provideTestEvaluateSilently() {
+        return [
+            [
+                new Expr\BinaryOp\Mod(new Scalar\LNumber(42), new Scalar\LNumber(0)),
+                \Error::class,
+                'Modulo by zero'
+            ],
+            [
+                new Expr\BinaryOp\Div(new Scalar\LNumber(42), new Scalar\LNumber(0)),
+                \ErrorException::class,
+                'Division by zero'
+            ],
+        ];
     }
 }