A numerical investigation was carried out to solve the flow dimensionless partial differential equations through rectangular microchannels. A purely viscous power law model was used to characterize the flow behavior of non-Newtonian fluids. The flow was assumed to be steady and laminar, and slip conditions were used as boundary conditions at the walls. The problem was solved for different power law indices as well as for various rectangular aspect ratios. Results showed that the effects ofslip velocity on dilatant fluids are more pronounced than that for pseudoplastic fluids. An increase in the power law index enhances the product of the friction factor and the Reynolds number, as well as the dimensionless incremental pressure drop and the dimensionless maximum velocity, while the hydrodynamic entrance length decreases. Results emphasize the significant effects of channel aspect ratio on the hydrodynamic flow behavior through microchannels.