The aim of dissertation is to create theoretical foundations and construct appropriate algorithms that allow the modeling of optical effects of dynamic visual cryptography in deformable and two-dimensional moiré gratings. The object of the research is the development of dynamic visual cryptography-based numerical image hiding algorithms in deformable harmonic, chaotic and two-dimensional moiré gratings. New methods of dynamic visual cryptography have been proposed in the thesis, where a deformed moiré grating oscillates harmonically and chaotically according to a certain Eigen-shape. A detailed analysis of these new methods opens the possibilities of applying the proposed methods for optical control of micro-opto-electromechanical systems. The most important element of the scientific novelty of this dissertation is the realization of dynamic visual cryptography in two-dimensional finite element gratings. In the works known so far, the principle of dynamic visual cryptography-based image hiding was based on the formation of time-averaged moiré fringe in one-dimensional moiré gratings. Applying image coding algorithms to two-dimensional gratings greatly expands the scope of the presented algorithms that constitutes the practical value of this dissertation.