An estimate of the effect of initial damage, such as delamination in the area of a structural hole, on the static and fatigue strength of polymer composite material (PCM) based on computational mechanics methods is presented. Calculation for durability of structural elements made of PCM is conducted using Simcenter 3D—Samcef package and Specialist Durability module. A typical carbon fiber-reinforced plastic with the available physical and mechanical characteristics obtained from the tests was chosen as the study material. Fatigue characteristics of the typical carbon fiber-reinforced plastic were approximated for subsequent calculation on durability. In the durability calculation, the observed parameter is the degradation of the material stiffness under repeated loading of the investigated area. The convergence with the experimental results of the fatigue strength modeling for a defect-free sample, which is a strip with a hole, is estimated. The fatigue strength of a sample with a delamination-type defect is also compared with the fatigue strength of a damage-free sample.