Nuclear power plants components are submitted to temperature variations due to startups and shutdown, step or ramp load changes, maintenance. These effects causes variations of temperature on pipe wall, which are known to induce thermal stress in structural components. As consequence, most solicited areas and/or stress concentration areas may suffer fatigue damage. Studying critical areas, make it possible to estimate the number of cycles and obtain the cumulative usage factor, CUF. This monograph will present fatigue damage calculations for a simple thick walled pipe according to the ASME Code. Structural stresses acting on a specified section on the wall thickness will be calculated using a finite element analysis (FEA). This result will be compared to a specific analytical solution proposed by Albrecht. Stress values will be linearized, calculated the number of cycles and obtained the value of CUF. The fatigue damage solution proposed by the ASME Code will be compared to the ones most traditional presented in literature about fatigue.