Wear is one of the main reasons for failure of modular total hip replacements. Recent evidence suggests that fretting wear occurs at the taper junction which provides fixation between the prosthesis femoral head and stem components. The fine metallic wear debris that is released can lead to adverse soft-tissue reactions which can necessitate a revision surgery. The present study proposes a computational methodology utilising an energy wear law and a 3D finite element model to predict fretting wear at the taper junction. The method is novel in that it simulates the weakening of the initial taper 'fixation' (created at impaction of the head onto the stem in surgery) due to the wearing process. The taper fixation is modelled using a contact analysis with overlapped meshes at the taper junction. The reduction in fixation is modelled by progressive removal of the overlap between components based on calculated wear. The fretting wear analysis approach has been shown to model the evolution of wear effectively; however, it has been shown that accurate, quantitative values for wear are critically dependant on mesh refinement, wear scaling factor and fraction, wear coefficient used and knowledge of the device loading history. The method has been implemented with a 3D finite element model of the taper junction of a commercial total hip replacement. This has been used to determine taper wear patterns, wear damage and wear rates which have been shown to be consistant with those found from observation and measurement of retrieved prostheses. The numerical method could be used to consider the effect of design changes and clinical technique on subsequent fretting wear in modular prosthetic devices.