Two-dimensional laminar flow of power-law fluids past a long square cylinder confined in a planar channel is investigated numerically for the range of conditions as 60 <= Re <= 160, 0.5 <= n <= 1.8 and beta = 1/6, 1/4, and 1/2. A semi-explicit finite volume method is used on a non-uniform collocated grid arrangement. The third order QUICK scheme and the second-order central difference scheme are used to discretize the convective and diffusive terms respectively. Depending upon the value of blockage ratio, power-law index and Reynolds number, the nature of flow in the above range of conditions is either steady or unsteady (periodic in time). An increase in the blockage ratio delays the onset of vortex shedding to higher Reynolds number in both shear-thinning and shear-thickening fluids whereas it advances the occurrence of the quasi-periodicity in flow to lower Reynolds numbers in shear-thinning fluids. Extensive numerical results are presented to elucidate the effects of blockage, power-law index and Reynolds number on the drag coefficient, stream function, vorticity, Strouhal number and amplitudes of drag and lift coefficients in the unsteady flow regime. (C) 2010 Elsevier B.V. All rights reserved.