The two-dimensional flow of power-law fluids over an isolated unconfined square cylinder has been investigated numerically in the range of conditions 1 <= Re <= 45 and 0.5 <= n <= 2.0. The global quantities such as wake length, drag coefficients and the detailed kinematic variables like stream function, vorticity and so on, have been calculated for the above range of conditions. In particular, the effects of Reynolds number and of the power-law index have been investigated in the steady flow regime. The shear-thinning fluid behaviour increases the drag above its Newtonian value whereas the shear-thickening behaviour reduces the drag below its Newtonian value. However, as the value of the Reynolds number is gradually increased, the role of power-law index diminishes. Similarly, the wake size is shorter in shear-thinning fluids than that in Newtonian fluids under otherwise indentical conditions.