The article is devoted the task of the circular cylindrical shell, is perceiving uniformly distributed load. The shell made of material with complicated properties, it has the property of different resistance and orthotropic. The article shows the system of resolving equations of the problem of research, supplemented by the boundary conditions. Gives the solution of the specific task of bending of the shell, shows most typical results of a study of stress-strain state and the analysis of results of calculation by the classical theory under constant mechanical characteristics with data by the proposed model under different resistant.