This　paper　presents　a　theoretical　study　and　finite　element　simulation　for　the　buckling　of　a　thin　film　on　the　compliant　substrate.　First,　we　develop　a　continuum　mechanics　approach　for　large　deformation　buckling　analysis　based　on　minimizing　the　total　energy　of　the　film/substrate　structures,　and　considering　the　precise　curvature　of　the　buckled　film　and　the　Poisson＇s　ratio　of　the　substrate.　The　predicting　results　using　this　proposed　theory　agree　quite　well　with　previous　experimental　results.　Then,　we　make　a　modification　for　the　model　to　simplify　the　expressions　for　the　wavelength　and　amplitude　of　the　buckled　geometry.　Furthermore,　considering　a　thin　Si　film　on　shape　memory　polymer　(SMP)　substrate,　we　investigate　the　buckling　behavior　of　the　thin　film　through　theoretical　analysis　and　finite　element　method.　Through　the　Investigation,　It　Is　found　that　the　evolution　rate　of　the　buckling　geometry　of　thin　film　depends　on　the　temperature　of　the　SMP　substrate,　and　the　buckling　geometry　changes　faster　at　a　higher　temperature.　Finally,　a　programmed　method　to　control　the　buckling　of　thin　Si　film　on　the　SMP　substrate　is　proposed　and　is　realized　with　finite　element　simulation　in　ABAQUS.　(C)　2017　Elsevier　Masson　SAS.　All　rights　reserved.