The creation of mobile miniature robots is an advanced and promising branch of modern engineering. The most important issues in the design of such robots are the development of propulsion and energy systems. The use of miniature electromechanical systems in the technological world is growing rapidly. Considering new applications the piezoelectric drive is a practical base to create miniature robots which move on different surfaces and in different media. Due to the small dimensions and low energy supply the development of piezoelectric platforms for miniature robots in the form of spheres, cylinders, plates with support rods can effectively solve many theoretical and practical problems. To study complex stress-strain states of plate-platforms for miniature robots methods of numerical analysis (finite element calculation) are used. This allows to obtain solutions of boundary value problems for plates with various shapes in conditions of a controlled resonance. This results can be compared with experimental data. This approach leads to a significant reduction of the design costs.