Numerical study was performed for the two-dimensional driven cavity flows of Ostwald-de Waele power-law fluid. For the computation of the flows, newly developed higher-order accuracy numerical code was utilized. The numerical solutions were obtained for a range of Re where viscous dominant creeping flows to the boundary layer flows appear. The value of the power m is varied in a wide range of 0<m≤2. The outcome of the numerical simulation suggests that the features of the flow when m≪1 is qualitatively very different from that of the Newtonian fluid flows.