An attempt to clarify the behavior of grease lubrication between two cylinders under heavy loads is described. The hydrodynamic equation of a Bingham solid and elasticity equation are solved simultaneously by a simplified method to discuss how the core formation in a Bingham flow affects the film thickness and the pressure of the elastohydrodynamic lubrication. The pressure dependencies of a plastic viscosity and a yield stress are included in this analysis and their effects are also discussed. It is found that the larger yield stress produces the larger film thickness under a certain load and velocity, and that the pressure dependence of a plastic viscosity rather than that of a yield stress affects the film thickness largely. Experiments are carried out to compare with the analytical results.