For　the　topology　optimization　problems　of　continuum　structures　with　stress　constraints,　an　adjoint　method　for　the　sensitivity　analysis　of　stresses　are　derived.　With　an　example,　the　results　of　the　sensitivity　analysis　of　the　stresses　by　the　presented　adjoint　method　are　compared　with　those　of　the　finite　difference　method;　and　it　verifies　the　accuracy　of　the　formula　of　the　adjoint　method.　Meanwhile,　it　is　shown　from　the　results　of　stress　sensitivity　analysis　that　the　partial　derivatives　of　stresses　with　design　variables　are　local.　On　this　basis,　taking　the　structural　topology　optimization　problem　with　minimizing　weight　as　the　objective　and　subject　to　stress　constraints　for　example,　the　effects　on　the　optimization　are　compared　between　the　first-order　Taylor　approximation　of　the　stress　and　the　fullstress　method.　The　results　show　that　the　first-order　approximation　of　stresses　can　make　the　stresses　of　more　parts　of　the　structure　reach　the　allowable　stress,　and　the　weight　of　the　optimal　structure　is　lighter　than　that　of　the　fullstress　method.　The　number　of　design　variables　for　the　topology　optimization　problems　of　continuum　structures　with　stress　constraints　is　usually　very　large.　The　number　of　stress　constraints　can　be　reduced　by　the　selection　of　quasi-effective　stress　constraints　and　there　is　no　need　to　consider　those　stress　constraints　of　the　deleting　elements.　Therefore,　the　number　of　stress　constraints　is　usually　smaller　than　that　of　the　design　variables,　and　the　adjoint　method　of　stress　sensitivity　analysis　can　significantly　improve　the　computational　efficiency.　©　2017,　Editorial　Department　of　CJAM.　All　right　reserved.