The momentum and forced convection heat transfer characteristics for an incompressible and steady free stream flow of power law liquids past a square cylinder have been investigated numerically. The momentum and energy equations have been solved by using a finite difference based numerical solution procedure for a range of rheological and kinematic conditions as follows: power law index, n: 0.5 to 1.4 thereby covering both shear-thinning and shear-thickening behaviour, Reynolds number (based on cylinder size), Re: 5 to 40 and Peclet number, Pe: 5 to 400. However, all computations have been performed for one blockage ratio L/H= 1/15. Furthermore, the influence of the type of thermal boundary condition, i.e., the constant heat flux and the constant temperature at the surface of the cylinder, has also been studied. Overall, when the drag coefficient and Nusselt number are normalized using the corresponding Newtonian values, these ratios show only marginal additional dependence on the flow behaviour index. The shear-thinning not only reduces the size of the wake region but it also delays the wake formation and shear-thickening behaviour shows the opposite effect. © 2003 Elsevier Ltd. All rights reserved.