The solution of bending tasks finite bodies with mixed boundary conditions. A new method for their research with direct (taking into account the current capabilities of computers) using Lurie-Vorovich solutions. It presents the most typical results of numerical studies in a wide range of values of the physical, geometrical, power settings, and various static and kinematic conditions on the lateral surface. We discuss the validity of the results and estimated solution of the classical two-dimensional thin plate bending theory.