In　this　paper,　a　new　nonlinear　model　of　nanobeams　made　of　bi-directional　(2D)　functionally　graded　material　(FGM)　is　presented.　The　material　properties　are　assumed　to　obey　an　exponential　gradation　along　both　the　thickness　and　length　directions.　The　equation　of　motion　is　derived　based　on　Euler-Bernoulli　beam　theory,　von　Korman　geometric　nonlinearity　and　non-local　elasticity　theory.　The　nonlinear　bending,　buckling　and　vibration　of　the　nanobeams　with　size　effect　is　investigated.　Results　show　that　the　2D　FGM　introduces　an　additional　stiffness　term　in　governing　equation,　so　it　cannot　be　solved　by　classical　analytical　methods.　Therefore,　the　differential　quadrature　method　(DQM)　is　used　to　solve　the　nonlinear　problem.　The　size-dependent　nonlinear　critical　load　and　frequencies　are　calculated.　The　effect　of　different　material　parameters,　boundary　conditions　and　size　scale　are　discussed　in　details.