Hydrodynamic lubrication of a bilinear theological fluid plays an important role in the so-called electrorheological (ER) ＇＇smart＇ bearings. There may not, however, be a reliable and efficient algorithm for the non-Newtonian lubrication problem of bilinear theological fluids. In this paper, a finite element method (FEM), together with a mathematical programming solution technique, are proposed for solving such a non-Newtonian lubrication problem. This method was used to study the hydrodynamic lubrication of a journal bearing lubricated by a bilinear theological lubricant. The computed results were compared with Tichy＇s work for the Bingham theological model. It was shown that the Bingham model should be regarded as a limiting case of the bilinear theological model.