<p>Based on the simplest mathematical model of free oscillations of an elastic plate, a numerical-analytical method for studying its dynamics in the case of hinged fastening of the ends has been developed. The model is described by a partial differential equation; we search for a solution by the Bubnov–Galerkin method. The purpose of the study is to determine the error of the obtained approximate solution using a Lyapunov-type functional. Numerical experiments have been conducted to confirm the reliability of the proposed method.</p>