High-speed hydrodynamic processes and phase transitions of “explosive character” developing in a result of an impulse penetration of short cryogenic nitrogen jets in a water were researched . The experimental researches were carried out on the base of a special scheme of tiny cryogenic “dewar”. The latter includes an external cryogenic shell, internal work cylindrical channel filled with a test sample of cryogenic nitrogen restricted by piston from above and by a diaphragm below. Impact of a piston on a liquid nitrogen column destroys the diaphragm and pushes out jet in a water. Dynamics of flow formation and of its structure arising in a result of cryogenic jet penetration as well as the influence of phase transitions were being recorded by high-speed digital video-camera. The experiments were carried out for two jets diameters - 1.5 to 10 mm. It was shown that jet penetration was accompanied by formation of initially open track (cavern, as at cumulative jet penetration) the internal surface of which turned out to be plated (covered) by layer of intense evaporating cryogenic nitrogen. Instability of track shape results in the chain formation of cavities comprising cryogenic and gas nitrogen mix. Their dynamics was experimentally studied. Change of the penetration velocity and of jet diameter allows one to get a thin tracks and to use their shape instability to form the clusters as the discrete systems of cryogenic nitrogen droplets. One of the main problems arising at mathematical simulation of the processes accompanying physical explosions is their kinetics. Its physical model can be formulated on the results of experimental researches or (as well as) of numerical analysis of "phase explosion" of cryogenic nitrogen drop at its ”instantaneous” contact with a water. It will allow one to create, in particular, the state dynamics model of discrete structure of cryogenic drops cluster under ”instantaneous” contact with a water. The experimental results and possible mathematical models will be discussed. (Supp. in part, ID Project 119, SB RAS, RF)