An advanced method for calculating crack growth in plate-like and axisymmetric structural elements under repeated loading conditions modeled using elastic–plastic material behavior, based on the principle of accumulation of distributed damage in the material is proposed. Near the crack tip, the processes of alternating elastic-plastic deformation and crack resistance of the material are modeled based on experimental results obtained from fatigue testing on smooth samples. Finite element analysis is conducted to determine the thermal and mechanical responses of the structure under different loading conditions. To assess accumulated metal damage from low-cycle fatigue, an improved method is used that takes into account the loading history. The ranges of equivalent elastic-plastic deformations are determined according to the Neuber’s rule. Damage is assessed using low-cycle fatigue curves based on the hypothesis of linear damage accumulation. At the same time, crack propagation during both the tensile and compressive stages and possible contact between the crack edges are taken into account. As the damage accumulates to a critical magnitude at the crack tip, the material is considered destroyed, and the crack grows stepwise. The developed method has significant advantages, since it does not impose restrictions on the size of the plastic zone and small crack depth. The results of calculations are compared with data obtained using the Newman’s formula.