An energy approach based on minimum entropy production has been taken in the analysis of the interface shape of vertical bicomponent flow of power‐law fluids. The sheath‐core and single flat interface configurations have been examined for the slit flow geometry in detail. Numerical calculation shows for similar materials of unequal Newtonian viscosities the sheath‐core configuration has a lower rate of entropy production subject to the appropriate constraint. The analysis is also outlined in considerable detail for the cylindrical tube case. The effect of different surface tensions is also examined for the nonflow situation.