The momentum transfer characteristics of a cone translating in power-law fluids in two different orientations (apex downward and apex upward) with reference to the direction of the mean flow is numerically investigated over wide ranges of conditions: Reynolds number, 1 <= Re <= 100; power-law index, 0.4 <= n <= 1.8; and cone angle, 20 degrees <= a <= 150 degrees. The governing differential equations (continuity and momentum) are solved numerically. The numerical solution obtained is then postprocessed to infer the effect of orientation for a given cone angle on the wake and drag phenomena. Finally, the present values of the drag coefficient for each orientation are used to develop predictive correlations in terms of Re, n, and a.