During the running-in period of a boundary lubricated contact, the surface roughness will be dramatically changed, involving large plastic deformation and wear on the asperity summits. This paper presents a running-in model. The model is based on the Boundary Element Method (BEM) and will focus on the investigation of large plastic deformations. The BEM model is based on the minimization of the complementary potential energy and deals with the contact at interfaces. The BEM model used in this paper previously adopted a linearly elastic- perfectly plastic material model and was frictionless, therefore a correction factor is needed for the model to improve its ability to account for high friction and large plastic deformation. The correction factor is made by improving the yield criterion and is derived with the assistance of the Finite Element Method (FEM). Both the friction and the strain hardening mechanism taken from the real material are implemented in the FEM model; the load and the contact area are required to match in both simulations. With the correction factor, results are promising for the current model to simulate the running-in process.