1. In this investigation we derived three analytical formulae that represent the flow velocity profile (i.e. Eqs. 17 and 18) and the volumetric flow rate (i.e. Eq. for the flow of power law fluids in tubes of elliptical cross sections. 2. We tested these formulae by developing numerical algorithms corresponding to these formulae and the formulae passed these tests. 3. We tested the convergence of these formulae to three special cases representing three types of flow (i.e. the flow of Newtonian fluids in circular tubes, the flow of Newtonian fluids in elliptical tubes, and the flow of power law fluids in circular tubes) and the formulae passed these tests. 4. We inspected trends, tendencies and correlations indicated by these formulae and the results of all these inspections were sensible and as expected. 5. If there is any doubt about the validity of the proposals and formulae that we presented and derived in this investigation (i.e. mainly the proposal of stress function and Eqs. 17, 18 and 19), there should be no doubt about the value of these proposals and formulae as each one of these three formulae which are derived from the proposal of stress function represents three types of flow (i.e. circular Newtonian, elliptical Newtonian and circular power law) simultaneously, and this condensation of formulation should be very useful theoretically and practically (e.g. in modeling and coding).