diff --git a/src/Magnum/Trade/Test/MeshDataTest.cpp b/src/Magnum/Trade/Test/MeshDataTest.cpp
index 2f6bb90da..ba042b7a2 100644
--- a/src/Magnum/Trade/Test/MeshDataTest.cpp
+++ b/src/Magnum/Trade/Test/MeshDataTest.cpp
@@ -114,6 +114,11 @@ struct MeshDataTest: TestSuite::Tester {
     void constructIndexlessNotOwned();
     void constructAttributelessNotOwned();
 
+    #ifndef CORRADE_TARGET_32BIT
+    void constructIndicesOver4GB();
+    void constructAttributeOver4GB();
+    #endif
+
     void constructIndexDataButNotIndexed();
     void constructAttributelessImplicitVertexCount();
     void constructIndicesNotContained();
@@ -299,6 +304,11 @@ MeshDataTest::MeshDataTest() {
                        &MeshDataTest::constructAttributelessNotOwned},
         Containers::arraySize(SingleNotOwnedData));
 
+    #ifndef CORRADE_TARGET_32BIT
+    addTests({&MeshDataTest::constructIndicesOver4GB,
+              &MeshDataTest::constructAttributeOver4GB});
+    #endif
+
     addTests({&MeshDataTest::constructIndexDataButNotIndexed,
               &MeshDataTest::constructAttributelessImplicitVertexCount,
               &MeshDataTest::constructIndicesNotContained,
@@ -2245,6 +2255,29 @@ void MeshDataTest::constructAttributelessNotOwned() {
     CORRADE_COMPARE(data.attributeCount(), 0);
 }
 
+#ifndef CORRADE_TARGET_32BIT
+void MeshDataTest::constructIndicesOver4GB() {
+    /* For some reason 2500 doesn't trigger an assertion, 3000 does */
+    Containers::ArrayView<UnsignedInt> indexData{reinterpret_cast<UnsignedInt*>(0xdeadbeef), 3000ull*1000*1000};
+
+    MeshIndexData indices{indexData};
+    MeshData data{MeshPrimitive::Triangles, {}, indexData, indices, 5};
+    CORRADE_COMPARE(data.indices().data(), indexData.begin());
+    CORRADE_COMPARE(data.indices<UnsignedInt>().size(), indexData.size());
+}
+
+void MeshDataTest::constructAttributeOver4GB() {
+    /* For some reason 2500 doesn't trigger an assertion, 3000 does */
+    Containers::ArrayView<UnsignedInt> vertexData{reinterpret_cast<UnsignedInt*>(0xdeadbeef), 3000ull*1000*1000};
+
+    MeshData data{MeshPrimitive::Triangles, {}, vertexData, {
+        MeshAttributeData{meshAttributeCustom(15), vertexData}
+    }};
+    CORRADE_COMPARE(data.attribute(0).data(), vertexData.begin());
+    CORRADE_COMPARE(data.attribute<UnsignedInt>(0).size(), vertexData.size());
+}
+#endif
+
 void MeshDataTest::constructIndexDataButNotIndexed() {
     CORRADE_SKIP_IF_NO_ASSERT();
 
diff --git a/src/Magnum/Trade/Test/SceneDataTest.cpp b/src/Magnum/Trade/Test/SceneDataTest.cpp
index f50829087..e51e7de4e 100644
--- a/src/Magnum/Trade/Test/SceneDataTest.cpp
+++ b/src/Magnum/Trade/Test/SceneDataTest.cpp
@@ -139,6 +139,11 @@ struct SceneDataTest: TestSuite::Tester {
     void constructDeprecatedBoth2DAnd3D();
     #endif
 
+    #ifndef CORRADE_TARGET_32BIT
+    void constructMappingOver4GB();
+    void constructFieldOver4GB();
+    #endif
+
     void constructDuplicateField();
     void constructDuplicateCustomField();
     void constructInconsistentMappingType();
@@ -489,6 +494,11 @@ SceneDataTest::SceneDataTest() {
     addTests({&SceneDataTest::constructDeprecatedBoth2DAnd3D});
     #endif
 
+    #ifndef CORRADE_TARGET_32BIT
+    addTests({&SceneDataTest::constructMappingOver4GB,
+              &SceneDataTest::constructFieldOver4GB});
+    #endif
+
     addTests({&SceneDataTest::constructDuplicateField,
               &SceneDataTest::constructDuplicateCustomField,
               &SceneDataTest::constructInconsistentMappingType,
@@ -3533,6 +3543,30 @@ void SceneDataTest::constructDeprecatedBoth2DAnd3D() {
 }
 #endif
 
+#ifndef CORRADE_TARGET_32BIT
+void SceneDataTest::constructMappingOver4GB() {
+    Containers::ArrayView<UnsignedInt> mappingData{reinterpret_cast<UnsignedInt*>(0xdeadbeef), 3000ull*1000*1000};
+    Containers::StridedArrayView1D<UnsignedByte> fieldData{mappingData, reinterpret_cast<UnsignedByte*>(mappingData.data()), 3000ull*1000*1000, 0};
+
+    SceneData data{SceneMappingType::UnsignedInt, 1, {}, mappingData, {
+        SceneFieldData{sceneFieldCustom(15), mappingData, fieldData},
+    }};
+    CORRADE_COMPARE(data.mapping(0).data(), mappingData.begin());
+    CORRADE_COMPARE(data.mapping<UnsignedInt>(0).size(), mappingData.size());
+}
+
+void SceneDataTest::constructFieldOver4GB() {
+    Containers::ArrayView<UnsignedInt> fieldData{reinterpret_cast<UnsignedInt*>(0xdeadbeef), 3000ull*1000*1000};
+    Containers::StridedArrayView1D<UnsignedByte> mappingData{fieldData, reinterpret_cast<UnsignedByte*>(fieldData.data()), 3000ull*1000*1000, 0};
+
+    SceneData data{SceneMappingType::UnsignedByte, 1, {}, fieldData, {
+        SceneFieldData{sceneFieldCustom(15), mappingData, fieldData},
+    }};
+    CORRADE_COMPARE(data.field(0).data(), fieldData.begin());
+    CORRADE_COMPARE(data.field<UnsignedInt>(0).size(), fieldData.size());
+}
+#endif
+
 void SceneDataTest::constructDuplicateField() {
     CORRADE_SKIP_IF_NO_ASSERT();