Abstract. We investigate the dynamics of an elastic plate of finite dimensions. The three-dimensional field of dynamic transverse displacements of the plate is constructed as a solution of two-dimensional differential equations parametrically dependent on the transverse coordinate. We consider the cases of discrete and continuous sets of the initial and boundary conditions that are satisfied by the mean square criterion. We describe the features of the solution of the problems in unbounded space–time domains.

Keywords: thick elastic plates, dynamics of distributed parameter systems, mathematical simulation.