The　strain-Rotation　(S-R)　decomposition　theorem　provides　a　reliable　and　reasonable　theoretical　basis　for　geometric　nonlinear　analyses.　However,　the　mesh　distortion　is　inevitable　in　a　large　deformation　analysis　when　using　the　finite　element　method.　The　virtual　element　method　(VEM)　proposed　recently　is　applicable　to　general　polygonal　meshes.　In　the　study,　the　first　order　VEM　is　used　to　solve　2D　geometric　nonlinear　problem　upon　S-R　decomposition　theorem,　aiming　to　overcome　the　impact　of　mesh　distortion.　One　project　operator　is　derived　for　the　linear　elastic　problem　from　the　admissible　displacement　space　to　the　polynomial　displacement　space,　by　redefining　the　basis　function　of　the　polynomial　displacement　space.　The　incremental　variation　equation　based　on　the　updated　co-moving　coordinate　formulation　and　the　potential　energy　rate　principle　is　computed　according　to　the　computation　rule　of　the　bilinear　form　in　VEM.　The　discretization　equation　is　obtained　with　the　matrix　expression,　and　a　solution　program　is　coded　in　MATLAB.　The　proposed　method　is　employed　in　the　deformation　analysis　on　a　cantilever　beam　under　distributed　loads　and　on　a　thick　cylinder　under　uniform　internal　pressures,　by　using　a　general　polygonal　mesh　and　a　distorted　mesh.　Comparison　on　the　results　by　the　method　proposed,　and　those　from　the　published　literatures　and　of　ANSYS　shows　that　the　method　proposed　is　valid　regardless　of　the　mesh　distortion　and,　has　a　sufficient　numerical　precision.　In　conclusion,　the　method　proposed　is　robust　to　solve　2D　geometric　nonlinear　problems　based　on　S-R　decomposition　theorem.　©　2024　Tsinghua　University.　All　rights　reserved.