To appreciate the effectiveness of lubrication approximation for the non-Newtonian fluid, power law fluid flowing between nonparallel plates was investigated under condition with no inertia. First the flow problem was successfully reduced to a single ordinary differential equation, and then the above governing equation was solved numerically. Effectiveness of lubrication approximation with various power law indices below 1 and various diverged angles was investigated in terms of normalized flow velocity and ratio of the approximate to exact flow rate. As the power law index decreases and diverged angle increases, the error of lubrication approximation becomes increasingly larger. It was shown that the proper selection of the constitutive law should be considered first to make the lubrication approximation work.