AbstractCylindrical shells are frequently used in industrial constructions, for example in pipes, towers and masts and are often subjected to fatigue loading. Two common welded constructional details were studied: i) detail 1, the wall thickness transition with a circumferential butt weld and ii) detail 2, the welded ring stiffener. Both details are loaded with axial stresses due to N and/or M. In the new Eurocode prEN 1993‐1‐9:2021 three different fatigue design stress methods are provided in general. For these two constructional details, beside the modified nominal stress method, the hot spot stresses and effective notch stresses are determined with Finite‐Element‐Analyses, with variation of geometric parameters, like shell thickness t, radius‐over‐thickness‐ratio, t2/t1‐ratio at the thickness transition and thickness ts of the ring stiffener. Stress concentration factors for the different fatigue design stress methods are presented and the influence of the geometric parameters are investigated. Especially the difference between a plate with an infinite radius‐over‐thickness‐ratio and the pipe with a finite radius‐over‐thickness‐ratio is shown. Also, the influence of the shell thickness is investigated. For comparison of the three different methods the utilization factors of the hotspot stress method and the effective notch stress method are compared with those of the modified nominal stress method. A recommendation is given, which design stress method is appropriate for the two studied details, depending on the geometric parameters.