Abstract The third-order shear deformation plate theory is utilized to analyze the vibration and bending of the simply-supported magneto-electro-elastic rectangular plates. The obtained analytical solution is valid for both thick and thin plates, and for arbitrary variation of material properties in the thickness direction. The natural frequencies obtained by the present study are proved to be identical with available results provided in references, which validates and verifies our formulation and programming. Parametric studies are completed for varying material gradient profile and length-to-thickness ratios. Analyses for forced vibrations and static bending of a multiferroic plate with a sinusoidal spatial variation of the pressure applied on its top surface complete the paper.