Discrete element methods require appropriate models for particle-particle collisions. Usually, researchers use soft-sphere types of models where the collision dynamics is solved numerically. This makes the simulation computationally expensive. In this paper, however, we show a hard-sphere model that uses ready analytic formulas that relate the pre- and postcollisional velocities of the particles in contact. This hard-sphere model is an extension of an existing model that uses three input parameters. For this, we applied the linear-spring soft-sphere model, where analytic relations can be found. These relations were implemented into the standard hard-sphere model. As a result, we obtain a robust hard-sphere model that is more accurate than the standard one and is still computationally cheap.