The momentum equations describing the steady cross-flow of power law fluids past an unconfined circular cylinder have been solved numerically using a semi-implicit finite volume method. The numerical results highlighting the roles of Reynolds number and power law index on the global and detailed flow characteristics have been presented over wide ranges of conditions as 5 <= Re <= 40 and 0.6 <= n 5 2. The shear-thinning behaviour (n < 1) of the fluid decreases the size of recirculation zone and also delays the separation; on the other hand, the shear-thickening fluids (n > 1) show the opposite behaviour. Furthermore, while the wake size shows non-monotonous variation with the power law index, but it does not seem to influence the values of drag coefficient. The stagnation pressure coefficient and drag coefficient also show a complex dependence on the power law index and Reynolds number. In addition, the pressure coefficient, vorticity and viscosity distributions on the surface of the cylinder have also been presented to gain further physical insights into the detailed flow kinematics.