A concept based on relaxation of the hydrodynamic parameters is introduced to arrive at a computational model for the extreme non-equilibrium distribution function of carriers in multi-valley bandstructure. The relaxation times are taken to describe the evolution scale of the distribution function. The developed model is able to account for transport phenomena at the momentum relaxation scale. The model, together with the Monte Carlo simulation, is applied to obtain the electron distribution function in each valley of the lower conduction band in GaAs, and to study the evolution of the distribution function in GaAs subjected to rapid changes in field.