Abstract: The governing differential equations and the internal force expressions of anisotrophic parallelogram plates on elastic foundation are presented. According to symmetry, the problem is decomposed into symmetrical and antisymmetric parts, and for each part, two homogeneous solutions and a particular solution are given. The general solution, which is expressed as double Fourier series, is obtained by means of superposition. The present solution overcomes the flaw associated with other solutions using the double Fourier series. A formula accelerating the convergence of Fourier series is given as well.