It is well-known that fibres improve the performance of cementitious composites by acting as bridging ligaments in cracks. Such bridging behaviour is often studied through the fibre pullout tests. The relation between the pullout force versus slip end displacement is characteristic of the fibre-matrix interface. However, such a relation varies significantly with the fibre inclination angle. In the current work, we establish a numerical model to explicitly represent the fibre, matrix and the interface for arbitrary fibre orientations. Cohesive elements endorsed with mixed-mode fracture capacities are implemented to represent the bond-slip behaviour at the interface. Contact elements with Coulomb’s friction are placed at the interface to simulate frictional contact. Matrix spalling is modelled through material erosion. The bond-slip behaviour is first calibrated through pull-out curves for fibres aligned with loading direction, then validated against experimental results carried out by Leung and Shapiro in 1999 for steel fibres oriented at 30° and 60°. The proposed methodology provides the necessary pull-out curves for a fibre oriented at a given angle for multi-scale models to study fracture in fibre-reinforced cementitious materials.