In the theory of structural design, including the optimal one, where the deterministic approach dominates, it raises interest in considering more general problems in which situations are taken into account when information about the factors of the system being designed is of an uncertain nature. Uncertainty can have probable, fuzzy and inaccurate nature. To formulate and solve problems in these cases, a mathematical apparatus is needed that would have the ability to a priori take into account any kind of uncertainty. Under the influence of random factors, probability theory became popular in mechanics. Based on it, the theory of safety was developed. Accounting of the fuzzy description factors is possible within the framework of fuzzy sets theory. From the standpoint of this theory, the problem of determining the maximum value of the axial force that compresses a circular cylindrical isotropic shell under conditions of stability and strength is considered, with a fuzzy specification of the initial data - radius and thickness of the type "close to", "approximately". Under fuzzy modeling is meant the execution of such stages of research as fuzzification, analysis, simulation modeling, optimization. The fuzzification of these data is accomplished by introducing fuzzy numbers. For their description, the membership function is used, which has a triangular and Gaussian form. An optimization problem is formulated that relates to the class of ССР -models of uncertain programming. A computational algorithm for realizing the model based on the Monte Carlo method is given in the paper. Several numerical experiments to study the influence of fuzzy information on which the optimal projects were obtained - the maximum value of the longitudinal force acting on the structure, for specific levels of the possibility of performing a fuzzy event - satisfaction of the conditions of the bearing capacity are given. As higher a level of opportunity as closer result to the case of a deterministic problem. An increase in the values of the parameters leads to an increase in the deviation from the deterministic calculation results of the optimization problem. To assess the accuracy of the obtained numerical results in the form of verbal terms, the definition of the linguistic variable "Accuracy" was introduced as one of the variants of the author's expert evaluation. From the data obtained, it is possible to identify the permissible limits of the specification of "rough" initial data.