In this paper a multi-sphere as well as a polyhedral approach is investigated as method of shape-approximation within the discrete element method. The two approaches are compared against each other using an ellipsoidal particle impacting on a flat wall as a reference scenario. In general it is shown that there is a non-negligible effect of shape approximation on the temporal force evolution in normal and tangential direction. The occurrence of multiple contacts between the particles when approximated by a multi-sphere or a polyhedral approach is detected as a main source of differences between the exact solution and the solution of the approximated particles. A method to account for these effects is provided in order to increase the accuracy when complex particle shapes are used. Moreover the effect of shape-approximation accuracy on the accuracy of the results is investigated. For both approximation procedures higher accuracy levels in terms of particle shape representation do not automatically lead to more accurate results for normal and tangential forces in the investigated collision scenarios. It will be shown that the effects of a more accurate ellipsoid-surface approximation and higher numbers of contact points influence the quality of the results in opposite directions. (C) 2011 Elsevier B.V. All rights reserved.