Abstract: Vibrations of a square plate with periodically changing parameters are considered. The averaged fourth-order partial differential equation for plate deflection w is presented. Solution of the problem is obtained with the approximate theory. The approximate results are presented by analytical formulas. Asymptotic averaging (implemented in Wolfram Mathematica) and the finite element method (ANSYS) are used to determine the values of eigenfrequencies. Numerical and asymptotic results are compared.