Currently existing finite element (FE) Lagrangian models of elastic-plastic spherical contact are costly in terms of computing time to reach vanishing tangential stiffness at sliding inception. A coupled Eulerian-Lagrangian (CEL) model with explicit dynamic analysis is proposed to resolve this problem. The CEL model also avoids convergence problem caused by excessive distortion of elements in Lagrangian models. Static friction coefficient at sliding inception is investigated and compared with available experimental results. It is found that the proposed new CEL model is more efficient and accurate compared to previously published results of Lagrangian models.