This paper presents an accurate model for the normal force–displacement relationship between elastic–plastic spheres in contact for use in discrete element method (DEM) simulations. The model has been developed by analysing the normal force–displacement relationship between an elastic–perfectly plastic sphere and a rigid surface using the finite element method (FEM). Empirical relationships are found that relate the parameters of the new model to material properties. This allows the model to be used in the DEM for direct simulation of well characterised elastic–plastic materials without fitting parameters to experimental results. This gives the model an advantage over models in the literature for which fitting to experimental results is required. The implementation of the model into an existing DEM code is discussed and validated against the results from FEM simulations. The new model shows a good match to the FEM results and the DEM implementation correctly distinguishes between the loading, unloading and re-loading phases of contact between two spheres.