This article presents the results of strength calculation for a large air-filter structure consisting of a set of cylindrical fiberglass tanks assembled into a pyramid. Inside each tank, a filter element is fixed. The tanks are connected by pipes so that the polluted air is entering the first tank, is going further through all other tanks, and is purified by the filters located in them. The construction is static, and the stress states in the walls of each particular tank are formed by the deadweight of the tank, as well as by the weight of the tanks located above. Two approaches were executed. First approach: the whole structure’s (according to symmetry conditions, one-fourth of the structure was observed) stress state was simulated using the FEM (Finite Element Method) software SolidWorks. Second approach: equilibrium state of one tank calculation was realized. At first step, mutual contact forces between the tanks in filtering structure were calculated under the assumption about full rigidity (no deformability) of the tanks. The obtained contact forces were used as boundary conditions for each particular tank. At second step, all more heavily loaded tanks (i.e., all tanks in the first two layers) were separately numerically analyzed (using FEM software SolidWorks). The model and the calculated deformed states were carefully analyzed. A few more heavily loaded tanks were numerically investigated by observing each of them separately (using FEM (Finite Element Method) mesh) with contact interaction forces between them working as external local loading conditions. The first outer tank in the first bottom row of tanks was recognized as the most heavily loaded tank in the structure. An acceptable tank’s wall thickness corresponding to loads existing in the structure was obtained.