This paper presents two non-parabolic hydrodynamic model formulations suitable for the simulation of inhomogeneous semiconductor devices. The first formulation uses the Kane dispersion relationship, (ℏk)2/2m = W(1+αW). The second formulation makes use of a power law, (ℏk)2/2m = xWy, for the dispersion relation. The non-parabolicity and energy range of the hydrodynamic model based on the Kane dispersion relation is limited. The power law formulation produces closed form coefficients similar to those under the parabolic band approximation but the carrier concentration can deviate. An extended power law dispersion relation is proposed to account for band structure effects, (ℏk)2/2m = xW1+yW. This dispersion relation closely matches the calculated band structure over a wide energy range and may lead to closed form coefficients for the hydrodynamic model.