We study the driven cavity flow using the Navier slip boundary condition. Our results have shown that the Navier slip boundary condition removes the corner singularity induced by the no-slip boundary condition. In the low Reynolds number case, the behavior of the tangential stress is examined and the results are compared with the analytic results obtained in . For the high Reynolds number, we study the effect of the slip on the critical Reynolds number for Hopf bifurcation. Our results show that the first Hopf bifurcation critical Reynolds number is increasing with slip length. © 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.