Mechanical components often possess notches. These notches give rise to stress concentrations, which in turn increases the likelihood that the material will undergo yielding. The finite element method (FEM) can be used to calculate transient stress and strain to be used in fatigue analyses. However, since yielding occurs, an elastic-plastic finite element analysis (FEA) must be performed. If the loading sequence to be analysed with respect to fatigue is long, the elastic-plastic FEA is often not a viable option because of its high computational requirements. In this thesis, a method that estimates the elastic-plastic stress and strain response as a result of input elastic stress and strain using plasticity modelling with the incremental Neuber rule has been derived and implemented. A numerical methodology to increase the accuracy when using the Neuber rule with cyclic loading has been proposed and validated for proportional loading. The results show fair albeit not ideal accuracy when compared to elastic-plastic finite element analysis. Different types of loading have been tested, including proportional and non-proportional as well as complex loadings with several load reversions. Based on the computed elastic-plastic stresses and strains, fatigue life is predicted by the critical plane method. Such a method has been reviewed, implemented and tested in this thesis. A comparison has been made between using a new damage parameter by Ince and an established damage parameter by Fatemi and Socie (FS). The implemented algorithm and damage parameters were evaluated by comparing the results of the program using either damage parameter to fatigue experiments of several different load cases, including non-proportional loading. The results are fairly accurate for both damage parameters, but the one by Ince tend to be slightly more accurate, if no fitted constant to use in the FS damage parameter can be obtained.