Hot pressing mechanisms are reviewed with special interest in the hot consolidation of metallic glass powders that exhibit a perfect viscous flow above the glass transition temperatures. The total densification process is divided into three stages; neck growth stage, cylindrical pore stage and isolated pore stage, for each of which the densification model and the critical relative density, separating the three stages, are unequivocally represented. The kinetic equations for the densification during hot pressing by the viscous flow mechanism are derived from those hitherto proposed for the power-law creep mechanism, in which the index of the constitutive equation is set to be unity. The equations for the relative density as functions of the hot pressing time and pressure are provided for the three stages of densification. An application of the kinetic equations to a processing design of the hot consolidation of metallic glass powders is demonstrated. The proposed set of the three equations enables an estimation of appropriate pressure and time for the full consolidation of metallic glass powders. The influence of entrapped gas in the final stage of hot pressing is also discussed.