In recent years there are more and more structures made of composite materials, especially in the form of thin-walled shells, being applied in various fields of technology. When using composite materials such as concrete or fiberglass, reinforcing elements are often placed along the axes of the curvilinear coordinate system of the shell, and in this case, the structure can be considered as orthotropic. There are a lot of papers on the calculation of orthotropic shells, but they do not adequately investigate a number of important factors that influence the stress-strain state of the shell and its stability. In particular, the calculation of reinforced shells does not take into account such factors as in-plane shear, shear and torsional stiffness of ribs, etc. The paper presents the mathematical model of deformation of thin orthotropic shells of revolution, based on the model of Timoshenko – Reissner. The model takes into account the design of reinforcement with the shear and torsional stiffness of the ribs, geometric nonlinearity and also the irregular shape of the shell. Possibility of application of methods and algorithms which are used in the study of isotropic shells is shown. The presented model investigates the stress-strain state and stability of thin orthotropic reinforced shells of revolution more adequate.