The effect of non-homogeneity in a magneto electro elastic plate of polygonal cross sections is studied using the linear theory of elasticity. The wave equation of motion based on two-dimensional theory of elasticity is applied under the plane strain assumption of plate of polygonal shape, composed of non-homogeneous transversely isotropic material. The frequency equations are obtained by satisfying the irregular boundary conditions of the polygonal plate using Fourier expansion collocation method. The analytical results obtained in the physical domain have been computed numerically for Triangle, Square, Pentagon and Hexagonal plates. The results for stress, strain, displacements, induced electric and magnetic fields have been presented graphically.