The Poiseuille flow of incompressible power-law fluids past a circular cylinder placed midway between two parallel plates has been investigated numerically by solving the continuity and momentum equations using FLUENT (Version 6.2). Extensive results highlighting the roles of the Reynolds number (Re), the power-law index (n), and the blockage ratio (β) on the global and detailed flow characteristics have been presented over wide ranges of conditions (1 ≤ Re ≤ 40, 0.2 ≤ n ≤ 1.9, and 1.1 ≤ β ≤ 4). For a fixed value of the blockage ratio, the drag coefficient increases as the shear-thickening (n > 1) tendency of the fluid increases, whereas shear-thinning (n < 1) fluid behavior shows the opposite dependence. At small Re, this effect is observed to be very strong and it gradually diminishes as Re increases. The effect of Re diminishes for n > 1 with a decrease in β, whereas the dependence becomes stronger for n < 1. Individual drag coefficients also show qualitatively similar dependence on Re, n, and β. In addition, the streamline and pressure profiles have also been presented to provide further physical insights into the detailed kinematics of the flow. The wake size is observed to increase as the flow behavior index (n) decreases. Because of wall effects, the flow separation seems to be delayed in shear-thickening fluids, whereas the opposite trend was observed in shear-thinning fluids. While the pressure profiles are observed to be similar to that for an unconfined flow, the flattening of the pressure curve in the rear portion of the cylinder suggests sluggish pressure recovery due to wall effects. In contrast to an unconfined flow, the front stagnation pressure coefficient values can be negative in magnitude, under certain conditions. The dependence of the pressure coefficient on the flow behavior index intensifies in shear-thickening fluids with a decrease in the blockage ratio. © 2007 American Chemical Society.