An　analysis　on　the　nonlinear　dynamics　of　a　cantilever　functionally　graded　materials(FGM)　cylindrical　shell　subjected　to　the　transversal　excitation　is　presented　in　thermal　environment.　Material　properties　are　assumed　to　be　temperature-dependent.　Based　on　the　Reddy＇s　first-order　shell　theory,the　nonlinear　governing　equations　of　motion　for　the　FGM　cylindrical　shell　are　derived　using　the　Hamilton＇s　principle.　The　Galerkin＇s　method　is　utilized　to　discretize　the　governing　partial　equations　to　a　two-degree-of-freedom　nonlinear　system　including　the　quadratic　and　cubic　nonlinear　terms　under　combined　external　excitations.　It　is　our　desirable　to　choose　a　suitable　mode　function　to　satisfy　the　first　two　modes　of　transverse　nonlinear　oscillations　and　the　boundary　conditions　for　the　cantilever　FGM　cylindrical　shell.　Numerical　method　is　used　to　find　that　in　the　case　of　non-internal　resonance　the　transverse　amplitude　are　decreased　by　increasing　the　volume　fraction　index　N.