The hydrodynamic theory of viscous lubrication is studied from Navier-Stokes differential equations ,by the method of successive approximation based upon the smallness of the film thickness. It is found that the first approximation gives the Reynolds equation of viscous lubrication. To simplify the numerical nature of the solution of Reynolds equation, the equivalent variational problem is formulated. The approximate solution obtained from the variational problem involves only a very small error, but much less amount of numerical work.