The equations of motion have been solved numerically for the incompressible power law fluid flow past spherical and spheroidal solid particles. The finite element technique has been employed to obtain the velocity and pressure fields prevailing around a particle. These have been further processed to evaluate the individual contributions of pressure and viscous forces to the total drag on spheres and spheroids (prolates and oblates). Streamline plots showing the nature of flow and the gradual development of the wake region are also presented. The computed drag results encompass wide ranges of physical and kinematic conditions given by 1 greater-than-or-equal-to n greater-than-or-equal-to 0.4, 0.01 less-than-or-equal-to Re less-than-or-equal-to 100, and 0.2 less-than-or-equal-to E less-than-or-equal-to 5. Extensive comparisons are provided with previous theoretical and experimental results available in the literature.