The contact force calculation using in discrete element simulation is typically calculated by single spring and damping models. It is found that the commonly used linear model gives unrealistic behaviour. A non-linear model of Tsuji [4] combined with the correct separating time gives more realistic results. Single spring and damping does not allow particles with different surface properties. A double spring and damping model: each particle with a separate spring and damping, is presented in this paper so that the different surface properties of each particle can be taken into account, To simply the calculations for particles with different surface properties, two methods of matching double spring damping models to single spring-damping models are presented in this paper.