Abstract: Based on the six dimensional dynamical system for Oldroyd B flow between two concentric cylinders, the effect of polymer additives on oil film stability in journal bearing has been analyzed. The results show that the instability structure of weak elastic flow is similar to that of Newtonian flow. The homoclinic orbit bifurcation occurs with the increase of velocity. Compared to Newtonian flow, a small amount of polymer additive can contribute to delay the transition from laminar flow to turbulence.