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Molecular motors are proteins that excessively increase the efficiency of subcellular transport processes. They allow for cell division, nutrient transport and even macroscopic muscle movement. In order to understand the effect of motors in large biopolymer networks, e.g. the cytoskeleton, we require a suitable model of a molecular motor. In this contribution, we present such a model based on a geometrically exact beam finite-element formulation. We discuss the numerical model of a non-processive motor such as myosin II, which interacts with actin filaments. Based on experimental data and inspired by the theoretical understanding offered by the powerstroke model and the swinging-cross-bridge model, we parametrize our numerical model in order to achieve the effect that a physiological motor has on its cargo. To this end, we introduce the mechanical and mathematical foundations of the model, then discuss its calibration, prove its usefulness by conducting finite-element simulations of actin-myosin motility assays and assess the influence of motors on the rheology of semi-flexible biopolymer networks.