System compliance is one of the critical parameters which need to be accounted for precise measurement of loads and displacements from a fretting test rig, irrespective of whether it is fretting fatigue or fretting wear. The system compliance in a fretting setup consists of compliance due to driving element, driven element, and other intermediate subassemblies which are part of the load train. The issue becomes more pertinent in fretting applications which involve loads (of the order of a few Newtons) together with displacement amplitudes (of a few microns), where the stiffness of the system can affect the contact variables significantly. In general, the experimental setup is calibrated at the beginning and requisite corrections are made to account for the system rigidity, but there could be a gradual stiffness degradation over the time which could influence the accuracy of the results. In the present study, two-dimensional finite element analysis has been carried out for a representative fretting test setup which consists of a flat specimen in contact with a cylindrical pad and subjected to normal load and tangential displacement. The loading elements have been represented through the elastic springs whose stiffness can be varied in both tangential and normal direction, to understand the implications of system compliance on both normal and shear tractions. The results of the finite element model are validated with the analytical solutions proposed by Mindlin (J Appl Mech 16:259–268, 1949 [1]). © 2020, Springer Nature Singapore Pte Ltd.