The shrinkage kinetics of a conductive material (copper powder) under spark plasma sinter-forging conditions in the presence and absence of the electric current passing directly through the specimen is investigated from both experimental and theoretical points of view. The experiments on the current-assisted and current-insulated spark plasma sinter-forging are conducted using specially developed spark plasma sintering tooling which has a number of particular features. The tooling enables direct temperature measurement at the free lateral surface of a powder sample as well as the simultaneous insitu measurement of the radius and height of a porous cylindrical sample during spark plasma sinter-forging, rendering conditions of bi-axial dilatometry. The continuum theory of sintering-based constitutive model of free upsetting (hot forging with free lateral surface) is refined taking into account the obtained experimental data on the current-insulated mode of spark plasma sinter-forging. It is shown that the model framework traditionally utilized for the description of hot deformation of powder materials is not suitable for the simulation of the considered current-assisted spark plasma sintering modes. Thus, the necessity of the development of new, specific to spark plasma sintering, constitutive models taking into account the direct contributions of electric current into mass transfer, is demonstrated.