Discrete element models can be widely applied in simulation of many types of physical systems including mineral processing and mining. The simulation process requires the calculation of the motion of each discrete element. The existing calculation methods are time consuming and often have been simplified to give unrealistic behaviour. A fast calculation method using a realistic force model has been developed. This method separates the solution of the differential equation of motion from the discrete element simulation process. It can result in improved accuracy and speed in certain types of simulations.