Currently much attention is paid to the analysis of the behavior of flexible plates and shells. First of all, researchers are attracted by the problem of determining the stress-strain state and stability of these structures. Problems of static stability occupy a special place. The processes of buckling and subsequent deformation of shells usually lead to the loss of their bearing capacity. At the same time, structures of different geometries are deformed in different ways. Therefore, the shape of the considered structures is also of great importance for the study of their stress-strain state and stability.The method of solving static problems of nonlinear deformation, buckling, and postbuckling behavior of thin elastic inhomogeneous shells is based on the geometrically nonlinear equations of the 3D thermoelasticity theory and use of the moment finite-element scheme (MFES) [1][2][3]. A model of a linearly elastic continuous medium is used, the properties of which correspond to the generalized Duhamel-Neumann law. Large displacements with small deformations are assumed. A solid finite element (FE) with additional variable parameters has been developed. A unified calculation model based on the universal FE has been created. The model takes into account the multilayer structure of the material and the geometric features of the structural elements of the inhomogeneous shell: casing of varying thickness, ribs, cover plates, cavities, channels, holes, and sharp bends of the mid-surface. The problem of nonlinear deformation, buckling, and postbuckling behavior of inhomogeneous shells is solved by a combined algorithm that employs the parameter continuation method, a modified Newton-Kantorovich method, and a procedure for automatic correction of algorithm parameters.