Nonlinear　bending　analysis　was　performed　of　magnetoelectroelastic　(MEE)　composite　plates　under　a　mechanical　and　magnetoelectric　(ME)　load　by　using　von　Karman’s　nonlinear　geometric　equation　and　the　higher　order　shear　deformation　theory　(HSDT).　Nonlinear　higher　order　partial　differential　equations　for　MEE　plates　were　derived　by　using　Hamiltonian　equilibrium　equation.　The　MEE　plate　is　considered　to　have　clamped　boundary　condition.　The　nonlinear　high-order　equations　can　turn　into　algebraic　equations　through　Galerkin　method.　Then　the　effects　of　scale　effect　of　MEE　plate　(for　instance,　the　aspect　ratio)　and　external　load　(for　instance,　mechanical)　on　the　displacement　of　the　considered　MEE　plate　were　investigated.　©　2021,　The　Korean　Society　of　Mechanical　Engineers　and　Springer-Verlag　GmbH　Germany,　part　of　Springer　Nature.