Three-dimensional simulations on the flow and wake behaviour of shear-thinning non-Newtonian fluids past spherical particles are carried out using a computational fluid dynamics based solver with the aim to investigate the critical Reynolds numbers for the onset of steady axisymmetric flow separation point and steady non-axisymmetric flow separation point. The present solver is thoroughly benchmarked through the conventional steps of domain independence, grid independence, and validation of the existing literature results. Before obtaining the critical Reynolds numbers for the case of shear-thinning fluids, the same for the case of Newtonian fluids are obtained and found to be in excellent agreement with literature values. The major findings of this work indicate that for the case of shear-thinning fluids, the first critical Reynolds number for the onset of steady axisymmetric flow separation increases with the decreasing power-law index of the non-Newtonian fluids; whereas the reverse is true for the case of second critical Reynolds number at which steady non-axisymmetric flow separation occurs. Furthermore, the non-axisymmetry is observed in both xy and xz planes for power-law fluids when n = 0.61 and 0.54; whereas in the case of fluids with n = 0.87, 0.73 and 0.66, the non-axisymmetry is observed only along the xz plane. Finally, correlations are proposed for both the critical Reynolds numbers as function of the power-law behaviour index. (C) 2018 Elsevier B .V. All rights reserved.