Abstract <p>A mathematical model for determining the stress-strain state of an orthotropic cylindrical shell with an open profile is proposed, based on the finite element method. The shell is not considered thin or medium-thick, to which the technical hypotheses of Kirchhoff, Timoshenko, Ambartsumyan, or Vlasov do not apply. As an example of model implementation, rigid restraint along the contour of the generatrices is considered. The developed model is based on a three-dimensional stress-strain state and a physically nonlinear approach to accounting for the mechanical properties of materials, associated with their dependence on the type of stress state. In other words, the model is constructed taking into account the structural properties of the materials from which the shell is constructed. These properties manifest themselves in orthotropic composites, where, under loading, the components of the compliance tensor continuously vary from point to point as the ratios between the components of the stress tensor change, which can be interpreted as induced mechanical heterogeneity of the material. The relationship between second-rank tensors is derived from the strain potential formulated in the normalized space of the principal material axes of orthotropy. These features of the problem somewhat complicate the calculations of spatial structures. Therefore, the developed mathematical model is based on isoparametric ten-node finite elements in the form of a tetrahedron with three degrees of freedom per node, the stiffness matrix of which was transformed to account for the mechanical properties of orthotropic materials. Due to the general nonlinearity of the resulting model due to the specific nature of the shell material, its numerical implementation was carried out using an iterative procedure of the variable elasticity method. As a result of implementing the computational model, the required set of parameters for the stress-strain state of the shell was obtained. The calculation results were compared with the characteristics obtained using the best-known equations of state for orthotropic materials with imperfect elasticity. A brief analysis of the obtained quantitative characteristics of shell deformation and its qualitative patterns is provided, taking into account various equations of state.</p>