In this article, free vibration studies on functionally graded, anisotropic and linear magneto-electro-elastic plates have been carried out by semi-analytical finite element method. A series solution is assumed in the plane of the plate and finite element procedure is adopted across the thickness of the plate such a way that the three-dimensional (3-D) character of the solution is preserved. The finite element model is derived based on constitutive equation of magneto-electro-elastic material accounting for coupling between elasticity, electric and magnetic effect. The present finite element is modeled with displacement components, electric potential and magnetic potential as nodal degree of freedom. The functionally graded material is assumed to be exponential in the thickness direction. The numerical results obtained by the present model are in good agreement with the isotropic 3-D exact benchmark solutions available in literature. Numerical study includes the influence of the different exponential factor, magneto-electro-elastic properties and effect of mechanical and electrical type of loading on induced magneto-electro-elastic fields. Further study has been carried out on higher harmonic. Study has been extended on functionally graded and layered magneto-electro-elastic plate. © 2006 Elsevier Ltd. All rights reserved.