There is formulation of the inverse problem of structural mechanics in the article. Optimal design of orthotropic cylindrical shell made of fiberglass, compressed with longitudinal forces is considered. The criterions of material-based restrictions are used. The restrictions are the strength, the local and overall buckling of the shell. The design variables are thickness, radius, and the relative content of reinforcing fibers. For the given compression force the analytical equations for the desired design parameters such as thickness, radius, relative content of reinforcing fibers and material volume (mass) of the shell are obtained. The convergence of the results using the Monte Carlo method was evaluated on the deterministic problem. An analysis of the influence of changes in the value of the compressive force on the value of the material minimum is made. The point of the value of the compressive force in which the minimum material volume function achieves its minimum is determined. On the basis of the theory of fuzzy sets and the obtained analytical solutions, a number of numerical experiments were carried out, in which the shell parameters were evaluated as a function of fuzzy value of force. As expected, the uncertainty in the original description of the data leads to an increase in the amount of the material. Implementation of tasks performed using the method of Lagrange multipliers and Monte Carlo method. According to the load the approach for coefficient of reliability estimation is proposed, taking into account the unfavorable deviation of the value and its real influence with the fuzzy description of the normative value. Model "load - bearing capacity" of the design is used. Investigation shows successful application of fuzzy sets and fuzzy modeling for described problem.