The momentum transfer characteristics of the power-law fluid flow past an unconfined elliptic cylinder is investigated numerically by solving continuity and momentum equations using FLUENT (version 6.2) in the two-dimensional steady cross-flow regime. The influence of the power-law index (0.2 <= n <= 1.8), Reynolds number (0.01 <= Re <= 40) and the aspect ratio of the elliptic cylinder (0.2 <= E <= 5) on the local and global flow characteristics has been studied. In addition, flow patterns showing streamline and vorticity profiles, and the pressure distribution on the surface of the cylinder have also been presented to provide further physical insights into the detailed flow kinematics. For shear-thinning (n < 1) behaviour and the aspect ratio E > 1, flow separation is somewhat delayed and the resulting wake is also shorter; on the other hand, for shear-thickening (n > 1) fluid behaviour and for E < 1, the opposite behaviour is obtained. The pressure coefficient and drag coefficient show a complex dependence on the Reynolds number and power-law index. The decrease in the degree of shear-thinning behaviour increases the drag coefficient, especially at low Reynolds numbers. While the aspect ratio of the cylinder exerts significant influence on the detailed flow characteristics, the total drag coefficient is only weakly dependent on the aspect ratio in shear-thickening fluids. The effect of the flow behaviour index, however, diminishes gradually with the increasing Reynolds number. The numerical results have also been presented in terms of closure relations for easy use in a new application. (c) 2007 Elsevier Ltd. All rights reserved.