The laminar flow of inelastic non-Newtonian fluids, obeying the power-law model, through a planar sudden expansion with a 1:3 expansion ratio was investigated numerically using a finite volume method. A broad range of power-law indices in the range 0.2 <= n <= 4 was considered. Shear-thinning, Newtonian and shear-thickening fluids are analyzed, with particular emphasis on the flow patterns and bifurcation phenomenon occurring at high Reynolds number laminar flows. The effect of the generalized Reynolds number (based on power-law index, n, and the inflow channel height, h) on the main vortex characteristics and Couette correction are examined in detail in the range 0.01 <= Re-gen <= 600. Values for the critical generalized Reynolds number for the onset of steady flow asymmetry and the appearance of a third main vortex are also included. We found that the shear-thinning behavior increases the critical Re-gen, while shear-thickening has the opposite effect. Comparison with available literature and with predictions using a commercial software (Fluent (R) 6.3.26) are also presented and discussed. It was found that both results are in good agreement, and that our code is able to achieve converged solutions for a broad range of flow conditions, providing new benchmark quality data. (C) 2013 Elsevier B.V. All rights reserved.