[en] A procedure has been developed to determine the cumulative fatigue damage in structures experiencing complicated multi-axial stress histories. The procedure is a generalization of the rainflow method developed by Matsuishi and Endo for one-dimensional situations. It provides a consistent treatment of three-dimensional stress states that is especially suited to computer programming applications for the post-processing of finite element stress data. The procedure includes a unique method to account for the rotation of principal stresses with time during the stress history and for the cumulative fatigue damage resulting from partial stress reversals within a stress cycle. The general procedure and necessary equations for programming are presented. Comparisons are made with life predictions using Section III of the ASME Boiler and Pressure Vessel Code for two hypothetical multi-axial stress histories for which the principal stresses are rotating with time. These comparisons show that the cycle counting method provides a consistent unambiguous interpretation of the fatigue design procedure in the ASME Code for these cases. Finally, the fatigue life of a perforated plate, as analyzed by finite elements, is computed for the combination of several hypothetical stress histories. This example demonstrates the utility of the proposed method when used in conjunction with finite element programs