Due　to　the　variation　in　material　properties　through　the　thickness　of　functionally　graded　material　(FGM)　structures,　an　FGM　beam　simply　supported　at　both　ends　exhibits　characteristics　quite　different　from　those　of　a　FGM　beam　clamped　at　both　ends.　An　exact,　closed　form　solution　is　obtained　for　nonlinear　static　responses　of　FGM　beams　subjected　to　non-uniform　in-plane　thermal　loadings.　The　equations　governing　the　axial　and　transverse　deformations　of　FGM　beams　are　derived　based　on　the　nonlinear　classical　beam　theory　and　the　physical　neutral　surface　concept.　The　two　equations　are　reduced　to　a　single　nonlinear　fourth-order　integral-differential　equation　governing　the　transverse　deformation.　For　an　FGM　beam　clamped　at　both　ends,　the　equation　and　the　corresponding　boundary　conditions　lead　to　a　differential　eigenvalue　problem,　whereas　for　an　FGM　beam　simply　supported　at　both　ends,　an　eigenvalue　problem　does　not　arise　due　to　the　inhomogeneous　boundary　conditions.　This　consequently　results　in　quite　different　behavior　between　a　clamped　and　a　simply　supported　FGM　beams.　The　nonlinear　equation　is　directly　solved　without　any　use　of　approximation　and　a　closed-form　solution　for　thermal　bending　deformation　is　obtained　as　a　function　of　the　applied　thermal　load.　By　using　the　exact　solutions,　the　nonlinear　deformation　problems　for　buckling,　postbuckling　and　nonlinear　bending　of　the　beam　can　be　investigated.　Finally,　the　numerical　analyses　are　carried　out　to　investigate　the　effects　of　material　gradient　properties　and　thermal　loads　on　the　nonlinear　static　responses　of　FGM　beams.　©　2017,　Engineering　Mechanics　Press.　All　right　reserved.