Structural　topological　optimization　is　to　seek　the　best　path　of　transmitting　forces　for　structures.　The　topological　optimization　under　multiple　loading　cases　involves　the　balance　of　many　paths　of　transmitting　forces.　Based　on　the　Independent　Continuous　Mapping　(ICM)　method,　the　optimization　problem　under　multiple　loading　cases　is　solved　under　three　conditions,　namely　local　constraints,　global　constraints,　and　their　combination.　In　this　paper,　local　constraints　are　firstly　analyzed　by　envelope　method　and　average　method.　Secondly,　global　constraints　are　uniformly　calculated　with　mathematical　programming　(MP).　Thirdly,　local　and　global　constraints　are　processed　by　synthesizing　above　two　methods.　Finally,　the　results　are　compared.　From　the　present　numerical　examples,　it　is　shown　that　the　envelope　method　and　the　MP　or　their　combination　can　be　used　to　efficiently　model　and　accurately　simulate　the　topological　optimization　problem　under　multiple　loading　cases.