In the present investigation the results of the multiscale modeling of the spark plasma sintering processing by the finite elements method using COMSOL MultiphysicsTM are presented. The multiscale theoretical model is put forward based on the hypothesis of the deformation softening of the particle interfaces due to the intense localized Joule heating of the inter-particle contact areas. The micro-inhomogeneity of the temperature distribution and its effect on the constitutive behavior of conductive porous medium for the current assisted sintering is discussed. The presence of the substantial difference between the macroscopic temperature of sintering and the local temperature in contact areas is shown. The temperature difference between the center of a powder particle and the inter-particle contact area is used for the refined calculation of the shrinkage kinetics of a non-linear viscous powder compact. This macroscopic-level calculation estimates the influence of the electric current on the shrinkage kinetics during spark-plasma sintering.