The normal and tangential force-displacement (NFD and TFD) relationships between a viscoelastic sphere and a rigid plane are analysed using the finite element method (FEM). The normal force models commonly used in the literature are carefully examined in terms of the viscous stress profile at the contact patch, and are found to exhibit discrepancy with the FEM outcome. There are also problems in the tangential force models in the literature. Based on the theoretical analysis and FEM results, a new set of semi-analytical models for both the normal and tangential forces is proposed and shown to be effective in simulating a host of oblique collisions. The new models have an advantage that their parameters can all be directly determined from the material properties for viscoelastic spheres. (C) 2012 Elsevier B.V. All rights reserved.