The shear-thinning/thickening effects on the plane Couette-Poiseuille flow with a uniform crossflow are studied. The detailed solution procedures for both theoretical and numerical purposes are given. In order to clarify the difference between the Newtonian flow and the power-law flow, all cases of the plane Couette-Poiseuille flows with uniform crossflows for different power indexes are assigned to the phase diagram in the parameter plane corresponding to the Couette number and the crossflow Reynolds number. The effects of shear-thinning/thickening on the phase diagram are discussed. An important feature of the shear-thinning circumstance distinguished from the shearthickening circumstance is discovered.