Wear prediction remains a major challenge in tribology, particularly for anisotropic fibre-reinforced materials where contact-induced stresses, frictional interactions, and failure mechanisms depend strongly on structural orientation. Conventional wear models are largely developed for isotropic systems and therefore fail to capture the directional dependence of wear resistance observed in many biological and engineered composites. In this study, we present an analytical framework for predicting wear behaviour in orthotropic materials by coupling Hertzian contact mechanics with an orientation-dependent failure criterion based on the Tsai-Wu formulation. The model extends the framework proposed by Ning et al. by incorporating friction-induced shear stresses into the failure analysis, enabling the evaluation of direction-dependent wear behaviour. As a biological model system, locust tendons were selected due to their highly aligned chitinous fibre architecture, allowing systematic investigation of anisotropic mechanical and tribological properties as a function of fibre orientation. Nanowear experiments revealed pronounced orientation-dependent wear behaviour, with substantially higher wear resistance when sliding occurred parallel to the fibres or on the transverse fibre section, compared to perpendicular sliding across the fibres. The analytical model successfully captured the experimentally observed wear trends across the tested orientations. To further demonstrate the model's applicability to isotropic materials, epoxy resins with varying polymer-to-hardener ratios were also tested, and the model successfully captured the experimentally observed wear-resistance trends. Unlike conventional isotropic wear indices such as H³/E², our framework explicitly incorporates fibre orientation, friction-induced shear stress, and anisotropic failure strength. This proposed modelling approach can effectively capture wear resistance trends in both orthotropic and isotropic systems, providing a mechanistic framework for the analysis of biological materials and for the design of materials with improved wear resistance.