FE micro-models have been developed in order to determine contact, stress and strain conditions produced by a steel asperity sliding on the surface of a normally oriented fibre-reinforced polymer composite. A displacement coupling technique was introduced to model a "micro-environment" as part of a "macro-environment" and to get more realistic simulation results about the failure conditions in the composite structure, in comparison to the so far widely applied anisotropic analytical or numerical macro-models. On the basis of the results, conclusions may be drawn for the possible wear mechanisms of the fibre-reinforced polymer composite. Stress results in the vicinity of the fibers in the contact area show high shear loading of the matrix leading to the formation of stretched-out matrix wear debris. In addition, high repeated compression-tension stresses at the fibre/matrix interface near the surface can lead to fibre debonding phenomena. Considering the fibre ends in the contact region, high compression stresses at their rear edges can produce fibre cracking features. To study the wear mechanisms experimentally, a "single asperity" scratch test was also performed showing shear failure events of the polymer matrix, fibre/matrix debonding and fibre cracking effects, as expected from the modelling studies.