A finite-volume-based numerical method with a strongly implicit relaxation procedure is developed to solve the elastohydrodynamically lubricated point contact problem. The multigrid algorithm for the solution of the governing equations and the multilevel multi-integration technique for the elastic deformation equation are also developed within the finite-volume framework. The performance of the developed finite-volume method has been evaluated extensively. The proposed method has a computational complexity of O(n log n) where n is the total number of control volumes. Up to 6.18 GPa maximum Hertzian pressure case has been calculated and demonstrated.Presented at the 53rd Annual Meeting in Detroit, Michigan May 17–21, 1998