In strongly coupled adsorption plants prevails during the operation a non-stationary process by the continuous change between adsorption and desorption. Because of these process fluctuating mechanical stresses are generated in the plant components. The article describes an approach to the stress development at the critical points and a sufficient approximation to determine these stresses, while reducing the computational effort within reasonable limits. Because of the detailed findings on fatigue stress range and load cycles it is possible to evaluate the components of an adsorption plant regarding to the method of Palmgren and Miner in higher quality. The innovative evaluation is in accordance with the ASME code or AD-regulations.