Reliability　analysis　and　design　optimization　of　structures　have　been　gaining　a　significant　amount　of　attention　in　recent　decades.　Most　of　the　current　studies　are　based　on　linear　structural　analysis.　The　study　on　reliability　analysis　and　design　optimization　for　nonlinear　structures　has　not　been　well　explored.　This　paper　presents　studies　on　reliability　analysis　and　design　optimization　for　nonlinear　structures,　by　using　the　Kriging　based　method　and　First-order　reliability　method　(FORM).　Numerical　studies　on　nonlinear　reinforced　concrete　structures　and　steel　frame　structures　are　carried　out　to　verify　the　accuracy　and　efficiency　of　the　proposed　methods.　The　results　demonstrate　that　the　FORM　and　Kriging　based　methods　have　the　same　accuracy　as　those　from　Monte　Carlo　Simulation　(MCS)　method.　Reliability-based　design　optimization　(RBDO)　is　conducted　for　nonlinear　structures,　in　which　the　dimensions　of　structures　can　be　optimized　and　the　target　occurrence　probability　can　be　achieved.　Compared　with　FORM　based　RBDO　method,　the　Kriging　based　method　is　more　accurate　and　efficient.　The　response　sensitivity　is　not　required　in　the　Kriging　based　method,　which　makes　it　more　versatile.