Abstract: A high resolution finite volume method(FVM) for calculating power law non Newton fluid is presented in this paper. In order to avoid the singularities of viscosity at zero and infinite shear rates, where the apparent viscosity calculated by the power law will impose difficulty for simulation of the flows, a strategy of limiting the range of apparent viscosity is proposed. The finite volume method is tested by calculating two laminar flows of power law fluids, in a pipe and in a sudden expansion, respectively. The influence of power law index on the velocity distribution is also analyzed.