A set of viscoplastic constitutive equations is presented in this study to predict hot compressive deformation behaviour and densification levels of powder metallurgy (P/M) FGH96 nickel-base superalloy during direct powder forging (DPF) process. The constitutive equations make use of the elliptic equivalent stress proposed in porous material models, and unify the evolution of relative density, normalised dislocation density, isotropic hardening and flow softening of the powder compact. A gradient-based optimisation technique is adopted to determine the material constants using the experimental data obtained from Gleeble isothermal uniaxial compression tests of HIPed FGH96 at different temperatures and strain rates. The developed constitutive equations are incorporated into finite element code DEFORM via user-defined subroutine for coupled thermo-mechanical DPF process modelling. The constitutive equations benefiting from the viscoplastic densification model of the calibrated Abouaf, among the six studied porous material models, compare favourably with the experimental data, while the equations integrating the porous material model of Shima and Oyane provide excellent agreement with experiments in the low density outer region of the powder compact.