This work introduces a finite element model of a steel cable-reinforced conveyor belt to accurately compute stresses in the splice. In the modelled test rig, the belt runs on two drums and is loaded with a cyclic longitudinal force. An explicit solver is used to efficiently handle the high number of elements and contact conditions. This, however, introduces some issues of dynamics in the model, which are subsequently solved: (a) the longitudinal load is applied with a smooth curve and damping is introduced in the beginning of the simulation, (b) residual stresses are applied in regions of the belt that are initially bent around the drums, and (c) supporting drums are introduced at the start of the simulation to hinder oscillations of the belt at low applied forces. To accurately capture the tensile and bending stiffness of the cables, they are modelled by a combination of solid and beam elements. The results show that numerical artefacts can be reduced to an acceptable extent. In the region of highest stresses, the displacements are additionally mapped onto a submodel with a smaller mesh size. The results show that, for the investigated belt, the local maximum principal stresses significantly increase when this region of highest stresses comes into contact with, and is bent by, the drum. Therefore, it is essential to also consider the belt’s bending to predict failure in such applications.