It is known that in the process of deformation of shells depending on the level and duration of external influences may appear different properties of the material of construction: elasticity, plasticity, creep, etc. The manifestation of plasticity or creep leads to irreversible consequences. To design is an obviously strong and stable construction, it is necessary to exclude the possibility of manifestation of these properties.

That is why urgent and important tasks are the development of better models of deformation of ribbed shells and corresponding algorithms for research and analysis of the strength and stability of ribbed shells taking into account the different material properties.

In [1] we were actually obtained the equilibrium equations of elastic isotropic shallow shells [which are an integral part of the dynamics (movement) of these shells from the perspective of German-known principle of d'Alembert-Euler equations] with allowance for geometric nonlinearity, the discrete location of the edges, their width, the shear and torsional stiffness, as well as the effect of transverse shear and rotational inertia.

This paper presents the generalization, development and analysis of mathematical models proposed by the author in the case of shells of general form and taking into account the different properties of the material under static (both short-and long-term) stress.