The complex interaction between shock waves and two-phase interfaces can generate cavitation. In this study, the cavitation induced by the high-speed jet impact on the water surface was investigated. The mixture fluid is modeled using the barotropic equation of state under the framework of the two-phase flow model, which can describe the mixture of air, water, and vapor with any proportion. Through constructing a 1D Riemann problem for the impact-induced cavitation phase transition, it indicates that the coupling effect of multiple rarefaction waves emitted from the two-phase interface is responsible for the cavitation phase transition inside the liquid. Then, a 3D (three-dimensional) simulation regarding the impact of a high-speed jet on the water surface was conducted and validated against previous experiments that captured the cavitation phase transition phenomenon in the central region after the jet impact. The 3D simulation results revealed the spatial structure and development process of shock waves in detail. The coupling effects of shock waves and two-phase interfaces generate a ring-shaped rarefaction wave, which develops radially inward and superimposes, resulting in the formation of acorn-shaped cavitation bubble nuclei inside the water. The 3D simulation can provide spatial shock/rarefaction wave structures and internal flow details that have never been obtained in experiments, such as shock generation and propagation, rarefaction wave generation and center convergence, and the internal structure of acorn-shaped cavitation nucleation. Furthermore, the influence of the jet velocity on the cavitation intensity was analyzed, and a quantitative relationship was provided.