The main goal of this paper is developing the advanced numerical methods for stress analysis of structures with crack-like defects. The novelty of proposed research consists in application of hypersingular integral equations for solutions of a benchmark test, and in stress analysis of the fuel tank under harmonic loads during transportation from the place of manufacture to the launch site. Boundary and finite element methods have been used for the benchmark test, whereas the finite element method is applied for the fatigue strength analysis of the tank. The fatigue analysis with finite amplitude cyclic loading was carried out. That has showed a high service life, which allows the intact structure to be successfully transported. When the model penny-shaped crack was placed in the zone of maximum stresses, an essential drop in the expected service life before destruction has been observed. From the point of view of practical applications, it was enough to transport such structures over short distances. However, a long-distance transportation can cause the mechanism of fatigue cracks propagation inside the shell with subsequent depressurization and failure.