The study is concerned with developing laminar flow of a power-law fluid in a circular tube. The analysis extends the filled-region concept, used previously to study Newtonian fluid flow, to the more general class of power-law fluids. Flow is analyzed in both the inlet and filled regions using an integral boundary layer method. Results obtained provide the lengths of the entrance, inlet and filled regions as a function of the generalized Reynolds number and the power-law fluid index. In addition, the variations of the local friction factor, the pressure drop and the centerline velocity along the axial coordinate are also provided. The available models are compared with the present one on the basis of experimental data. The present results are found to reach asymptotically the fully developed values, and also to be in good agreement with all available experimental data.