The equations of motion and continuity of a fully developed, steady-state, isothermal, incompressible laminar flow of power law fluids within a toroidal-type coiled tube geometry have been solved numerically using the successive overrelaxation method. Numerical solutions have been obtained for curvature ratios from 5 to 100, Dean number from 1 to 300, and power law index from 0.5 to 1.5. Dean's constraint has been relaxed and the numerical solutions for primary and secondary flow, and the numerical results of the friction factor for different values of Dean number, curvature ratio, and power law index have been computed. The solutions have been carefully checked for accuracy and the results are compared with previous studies. The numerical results are found to be consistent with the published results for the case of Newtonian fluids. The ratio of friction factor of a curved tube to a straight tube increases with the Dean number and also with the power law index.