diff --git a/interp/interp.go b/interp/interp.go
index cab9d9e3..ba358384 100644
--- a/interp/interp.go
+++ b/interp/interp.go
@@ -145,6 +145,9 @@ func Run(mod llvm.Module, debug bool) error {
 		if obj.buffer == nil {
 			continue
 		}
+		if obj.constant {
+			continue // constant buffers can't have been modified
+		}
 		initializer, err := obj.buffer.toLLVMValue(obj.llvmGlobal.Type().ElementType(), &mem)
 		if err == errInvalidPtrToIntSize {
 			// This can happen when a previous interp run did not have the
@@ -248,6 +251,9 @@ func RunFunc(fn llvm.Value, debug bool) error {
 		if obj.buffer == nil {
 			continue
 		}
+		if obj.constant {
+			continue // constant, so can't have been modified
+		}
 		initializer, err := obj.buffer.toLLVMValue(obj.llvmGlobal.Type().ElementType(), &mem)
 		if err != nil {
 			return err
diff --git a/interp/memory.go b/interp/memory.go
index 61c83890..e358124e 100644
--- a/interp/memory.go
+++ b/interp/memory.go
@@ -41,6 +41,7 @@ type object struct {
 	globalName     string    // name, if not yet created (not guaranteed to be the final name)
 	buffer         value     // buffer with value as given by interp, nil if external
 	size           uint32    // must match buffer.len(), if available
+	constant       bool      // true if this is a constant global
 	marked         uint8     // 0 means unmarked, 1 means external read, 2 means external write
 }
 
@@ -223,7 +224,7 @@ func (mv *memoryView) hasExternalLoadOrStore(v pointerValue) bool {
 // possible for the interpreter to read from the object.
 func (mv *memoryView) hasExternalStore(v pointerValue) bool {
 	obj := mv.get(v.index())
-	return obj.marked >= 2
+	return obj.marked >= 2 && !obj.constant
 }
 
 // get returns an object that can only be read from, as it may return an object
@@ -263,6 +264,9 @@ func (mv *memoryView) put(index uint32, obj object) {
 	if checks && mv.get(index).buffer.len(mv.r) != obj.buffer.len(mv.r) {
 		panic("put() with a differently-sized object")
 	}
+	if checks && obj.constant {
+		panic("interp: store to a constant")
+	}
 	mv.objects[index] = obj
 }
 
@@ -1138,6 +1142,7 @@ func (r *runner) getValue(llvmValue llvm.Value) value {
 				obj.size = uint32(r.targetData.TypeAllocSize(llvmValue.Type().ElementType()))
 				if initializer := llvmValue.Initializer(); !initializer.IsNil() {
 					obj.buffer = r.getValue(initializer)
+					obj.constant = llvmValue.IsGlobalConstant()
 				}
 			} else if !llvmValue.IsAFunction().IsNil() {
 				// OK
diff --git a/interp/testdata/basic.ll b/interp/testdata/basic.ll
index d0af3af3..30c0bf08 100644
--- a/interp/testdata/basic.ll
+++ b/interp/testdata/basic.ll
@@ -6,6 +6,7 @@ target triple = "x86_64--linux"
 @main.nonConst2 = global i64 0
 @main.someArray = global [8 x {i16, i32}] zeroinitializer
 @main.exportedValue = global [1 x i16*] [i16* @main.exposedValue1]
+@main.exportedConst = constant i64 42
 @main.exposedValue1 = global i16 0
 @main.exposedValue2 = global i16 0
 @main.insertedValue = global {i8, i32, {float, {i64, i16}}} zeroinitializer
@@ -62,6 +63,11 @@ entry:
   call void @modifyExternal(i32* bitcast ([1 x i16*]* @main.exportedValue to i32*))
   store i16 5, i16* @main.exposedValue1
 
+  ; Test that marking a constant as external still allows loading from it.
+  call void @readExternal(i32* bitcast (i64* @main.exportedConst to i32*))
+  %constLoad = load i64, i64 * @main.exportedConst
+  call void @runtime.printint64(i64 %constLoad)
+
   ; Test that this even propagates through functions.
   call void @modifyExternal(i32* bitcast (void ()* @willModifyGlobal to i32*))
   store i16 7, i16* @main.exposedValue2
@@ -96,6 +102,8 @@ declare i64 @someValue()
 
 declare void @modifyExternal(i32*)
 
+declare void @readExternal(i32*)
+
 ; This function will modify an external value. By passing this function as a
 ; function pointer to an external function, @main.exposedValue2 should be
 ; marked as external.
diff --git a/interp/testdata/basic.out.ll b/interp/testdata/basic.out.ll
index 9279606e..5c68ec5e 100644
--- a/interp/testdata/basic.out.ll
+++ b/interp/testdata/basic.out.ll
@@ -5,6 +5,7 @@ target triple = "x86_64--linux"
 @main.nonConst2 = local_unnamed_addr global i64 0
 @main.someArray = global [8 x { i16, i32 }] zeroinitializer
 @main.exportedValue = global [1 x i16*] [i16* @main.exposedValue1]
+@main.exportedConst = constant i64 42
 @main.exposedValue1 = global i16 0
 @main.exposedValue2 = local_unnamed_addr global i16 0
 @main.insertedValue = local_unnamed_addr global { i8, i32, { float, { i64, i16 } } } zeroinitializer
@@ -24,6 +25,8 @@ entry:
   call void @modifyExternal(i32* bitcast (i8* getelementptr inbounds (i8, i8* bitcast ([8 x { i16, i32 }]* @main.someArray to i8*), i32 28) to i32*))
   call void @modifyExternal(i32* bitcast ([1 x i16*]* @main.exportedValue to i32*))
   store i16 5, i16* @main.exposedValue1, align 2
+  call void @readExternal(i32* bitcast (i64* @main.exportedConst to i32*))
+  call void @runtime.printint64(i64 42)
   call void @modifyExternal(i32* bitcast (void ()* @willModifyGlobal to i32*))
   store i16 7, i16* @main.exposedValue2, align 2
   call void @modifyExternal(i32* bitcast (void ()* @hasInlineAsm to i32*))
@@ -54,6 +57,8 @@ declare i64 @someValue() local_unnamed_addr
 
 declare void @modifyExternal(i32*) local_unnamed_addr
 
+declare void @readExternal(i32*) local_unnamed_addr
+
 define void @willModifyGlobal() {
 entry:
   store i16 8, i16* @main.exposedValue2, align 2