In Finite Element (FE) simulations of sheet metal forming (SMF), the coefficient of friction is generally expressed as a constant Coulomb friction. However in reality, the coefficient of friction at the local contact spots varies with the varying operational, deformation and contact conditions. Therefore, it is important to calculate the coefficient of friction under local conditions to better evaluate the formability of the product. Friction at a local scale is largely influenced by the micro-mechanisms at the asperity level like shearing in the boundary layer, ploughing and hydrodynamic lubrication. In this paper, a new mixed lubrication model is developed considering the aforementioned micro-mechanisms to better describe the friction conditions for deep drawing processes. Central to the friction prediction is the calculation of the lubricant film thickness and the contact area evolution based on the asperity flattening mechanisms. In deep drawing, asperity flattening can occur due to normal loading and stretching of the workpiece surface. Both flattening mechanisms are accounted in this model. The developed model is applied to an axi-symmetric cup drawing process. The results show that the coefficient of friction is not constant during the drawing process. Effects like asperity flattening and ploughing mechanisms increase the coefficient of friction under some conditions. Lubrication process decreases the coefficient of friction due to mixed lubrication effects.