A method is presented for modeling the cavity formation and collapse induced by high-speed impact and penetration of a rigid projectile into water. The approach proposes that high-speed water-entry is characterized by a cavity that experiences a deep closure prior to closure at the surface. This sequence in the physical events of the induced cavity dynamics is suggested by the most recent high-speed water-entry experimental data, by results from numerical experiments using a hydrocode, and by an understanding of the fundamental physics of the processes that govern surface closure. The analytical model, which specifies the energy transfer for cavity production as equivalent to the energy dissipated by velocity-dependent drag on the projectile, provides accurate estimates for variables that are important in characterizing the cavity dynamics, and reveals useful knowledge regarding magnitudes and trends. In particular, it is found that the time of deep closure is essentially constant and independent of the impact velocity for a given projectile size, while the location of deep closure has a weak dependence on impact velocity. Comparison of these analytical results with experimental results from the literature and with results from numerical simulations verifies the analytical solutions.