The study of a non-Newtonian fluid flow behavior in mixing cavities is of great importance in process industries. In the present work, a Bhatnagar-Gross-Krook (BGK) approximation based lattice Boltzmann method (LBM) is presented to simulate non-Newtonian power law fluid flows in a double sided lid driven cavity. First, the code is validated against numerical results taken from the published sources for power law fluid flow in cavity driven by the uniform motion of lid. Next, the code is applied for two different cases-parallel wall motion and anti-parallel wall motion of two sided lid driven cavity. The influence of power law index (n) and Reynolds number (Rea) on the variation of velocity and center of vortex location of fluid has been analyzed with the help of velocity profiles and streamline plots. Additionally, we also study the effect of speed ratio on development of vortex in a cavity. Further, the effect of n on variation of drag coefficient has been presented. Finally, we present the location of vortex center and computational time required for a system to reach the steady state. (C) 2012 Elsevier B.V. All rights reserved.