The numerical study of plasticity-induced crack closure using the node-release technique presents many difficulties widely studied in literature. For instance various rules, proposed for overcoming mesh sensi- tivity, are challenged by more recent studies. This paper intends to propose and evaluate a numerical method for the investigation of crack propagation under fatigue loading, and particularly for the assess- ment of plasticity-induced crack closure in three-dimension. The method is an extension of the ''steady- state method'' to cyclic loadings. The steady-state method allows a direct computation (on a fixed mesh, without releasing nodes) of stress and strain fields around the crack tip and in the wake for a steady crack growth. The method is extended to simulate crack propagation under fatigue loading. Therefore it con- stitutes a valuable numerical tool for gaining insight into the physics of crack propagation, as it provides accurate mechanical fields around the crack tip and their relation with crack growth rate, various loading modes and parameters. The proposed method is also compared with the classical node-release technique. A very good agreement between the two methods is found. However the steady-state method needs much less mesh refinement and computational time. Following an analysis of some features of the fatigue crack, a discussion on a crack closure criterion is opened, and a reliable criterion for the determination of local crack closure is proposed.