The article shows the possible ways of building mechanical and mathematical models of the behavior of deformable elastic media with regard to their internal structure. The constructions are made in the framework of continuum mechanics to static problems of deformation of elastic bodies. A significant factor in this is that the internal structure of the accounting environment does not allow a physical equations describing the behavior of the environment (the connection between the components of the stress-strain state), using Hooke’s law in standard form. The results performed on the basis of the proposed model, the numerical analysis of the stress-strain state of the model structure (plate) and then comparing the results with the behavior of structures whose state is described by the classical Hooke's elastic model.