The effect of vibration on soil compaction has gained a good reputation when consolidating an artificially improved foundation. The studies aimed at analyzing the effect of the deep vibration on the properties of the compacted water-saturated soil have made it possible to establish that vibration can be an effective means of consolidation speeding-up. Vibration contributes to the emergence of additional excess pressures in the pore water; the filtration rate due to the increased pressure gradient increases as well. Consolidation speeding-up (soil compaction by squeezing out the pore water) is quite relevant. It is clear that consolidation speeding-up of foundation water-saturated soil is extremely important in site preparation for reducing site preparation time up to a period of a short summer. The study focuses on the mechanism of deep vibration (longitudinal mechanical waves) having an effect on water-saturated soil consolidation. The mechanism is based on the changed physical state of the medium and takes into account its structure. Two soil models have been proposed. The first one-parameter soil model is called a