The　nonlinear　forced　vibration　of　bidirectional　functionally　graded　porous　material　beams　where　the　material　components　gradient　change　in　both　thickness　and　axial　directions　are　studied　in　this　study.　Combining　von　Karman＇s　geometric　nonlinearity　and　first-order　shear　deformation　theory,　the　governing　equations　describing　the　coupled　deformations　are　formulated　as　a　system　of　nonlinear　partial　differential　equations.　Utilizing　the　Galerkin　method,　the　formulated　continuous　model　is　transformed　to　a　coupled　nonlinear　ordinary　differential　dynamic　system.　By　accomplishing　bifurcation　calculation　for　periodic　response　of　the　discrete　system　using　pseudoarclength　technique,　the　vibration　response　curves　are　obtained　by　extracting　the　max-min　amplitude　of　periodic　motions.　To　highlight　the　effect　of　nonlinearity,　the　linear　and　nonlinear　dynamic　responses　of　beam　are　demonstrated.　It　is　found　that　the　periodic　motion　of　beam　may　undergo　cyclic-fold　bifurcation.　Numerical　results　are　presented　to　examine　the　effects　of　the　system　parameters,　e.g.,　gradient　indexes,　porosity,　damping　coefficients,　and　aspect　ratio.　Copyright　©　2021　Jianqiang　Wu　et　al.