An exact numerical solution to the 2-D（Two-Dimensional） laminar boundary-layer equations of power-law non-newtonian fluids is obtained using a finite difference technique. No limitation has been imposed on the flow behavior index(n) or generalized Prandtl number. As a test case, velocity and temperature fields around a circular cylinder in crossflow were calculated. The result clearly indicated that heat transfer of power-law materials is governed by shear dependent viscosity.