Abstract: In this Paper, an automate optimal design method in which Reynolds equation solved by the method of finite-element is regarded as a mathematical model is applied to the liquid film hydrodynamic lubrication for the journal bearings. By using the method of penalty function with conjugate directions,a combination of design parameters for the step bearings can be optimized. In this method, the load of the journal bearings is given, and an objective function is set up for the minimum frictional power dissipation or .the maximum stability. The developed program is versatile and flexible. It has brought about an economy of computing time to adopt effective measures. Therefore, it is practically feasible to take with the optimal design directly for the hydrodynamic bearings instead of using the conventional fitting method.