The steady state growth equation for a paraboloid of revolution and a parabolic cylinder, taking the interfacial energy into account, is revisited. Although the consideration of the interfacial energy was necessary, the growth equation was much more complicated than the original equation with a zero interfacial energy, since both the thermodynamics and kinetics of the growth are considered in one equation. In the present work, we take advantage of the development in computational thermodynamics and consider the thermodynamics and kinetics of the process in separate equations, but solve them simultaneously. A consistent framework to describe the phenomena and compare it with previous treatment of the interfacial energy will be presented. ©1997 American Institute of Physics.