The　stress　constraint　is　replaced　by　the　distortional　strain　energy　density　constraint　because　the　von　Mises　strength　criterion　was　essentially　established　on　the　distortional　strain　energy　density.　According　to　stress　globalization　strategy,　the　concept　of　a　structural　distortional　strain　energy　density　constraint　is　defined　and　it　is　applied　to　sharply　reduce　stress　constraints　in　solving　a　structural　topology　optimization　problem　with　least　weight　subjected　to　stress　constraints.　A　parameter-power　function　about　the　ratio　of　allowable　stress　to　maximum　stress　in　the　structure　is　constructed　to　modify　the　constraint　limit　dynamically.　Based　on　ICM　(Independent　Continuous　and　Mapping)　method,　an　exponential-class　fast　filter　function　is　adopted　to　present　a　structural　topological　optimization　model,　and　then　the　model　is　solved　by　sequential　quadratic　optimization　based　on　exact　dual　mapping.　The　numerical　examples　demonstrate　that　the　approach　of　adopting　globalization　strategy　of　modified　structural　distortional　strain　energy　density　to　deal　with　the　structural　topological　optimization　problem　with　stress　constraints　is　available　and　efficient.　The　method　proposed　in　the　paper　is　also　useful　to　solve　the　loading　illness　problem　between　different　loading　cases.