We propose a method for theoretical analysis of three-dimensional plate-like structures when the curve of deformation of a material is of non-linear character. We consider the case when displacements are comparable in magnitude with a thickness of structural elements of the system. We obtain principal non-linear differential equations of stability. The Runge-Kutta procedure is used for numerical integration of these equations. The Fortran programming language is employed. As an example, we consider a three-dimensional plate-like structure that is a uni-connected prismatic shell under torsion. We present curves of stress-strain state of the structure versus the load. Some kinds of linearity is considered.