The crack compliance method (eeM) has attracted a lot of interest as an inexpensive method for the determination of residual stresses in materials compared to the use of Xray and neutron diffraction methods. The vast majority of the work found for the application of the eeM in the literature concentrated on the determination of residual stresses in annealed beam specimens. There is very little evidence of the verification of the method in cases where the material might have experienced prior strain loading effect such as Bauschinger effect before the residual stress is induced. This thesis has applied the eeM for the determination of residual stresses in bemus that were under Bauschinger effect before the residual stress was induced. The thesis also briefly considers the application of the eeM for the study of cyclic loading effect on the relaxation of residual stresses in beams. In order to achieve the aims highlighted above, the thesis develops a new efficient solution for the simultaneous determination of tensile and compressive stress-strain behaviour in materials under Bauschinger effect. The determination of these properties helps with the verification of the results of the eeM by using another relatively simple and inexpensive method based on the superposition of loading and unloading stresses. A new simple support method for beams subjected to electro-discharge machining (EDM) is also introduced. The new cutting arrangement allows free deformation of beams during cutting and allows the plane of cutting to be maintained without deviation. The experimental testing and verification procedure considers several factors such as different materials, heat treatment conditions, various levels of pre-straining and different fatigue load amplitudes. Several aspects of the crack compliance method are verified. The results obtained in all cases are generally very encouraging.