High density particulate matter suspensions in water, such as mud layers and debris flows [1], quicksand [2] masses of liquids different from water driven by planetary atmospheric dynamics, such as liquid methane lakes in Titan, a moon of Saturn [3], are examples of environmental systems in which non-newtonian fluids can be driven by winds. In this work, wind-driven flow in power-law viscous fluids in homogeneous semienclosed basins is analyzed. Analytical and numerical solutions for vertical current profiles for non-newtonian fluids with different power-law indexes are derived assuming a wind shear stress at the surface and zero net transport. Previous classical solutions for wind-driven flows in semienclosed basins are thus generalized [4, 5]. A bidirectional flow in the fluid column is obtained: downwind near the surface and a compensating upwind flow near the bottom. The larger the flow behavior index n of the power-law, the more acute the effects. For the same physical conditions (depth, wind shear stress, and flow consistency index), the opposite occurs for shear-thinning fluids.