From the summary: We investigate some models focusing on hydrodynamic and elastic forces arising during the impact of rigid and elastic systems on the water surface. In particular, we consider the supersonic compressible stage of the impact by modelling the slamming phenomenon through the Skalak-Feit acoustic approximation. The dynamic equations of the dropping system are coupled to those of the fluid, and a nonlinear fluid-solid interaction problem is stated. We determine general relationships between the body’s shape, slamming force and body motion. These equations are applied to the wedge water entry, and a closed-form expression for the maximum hydrodynamic force is found. Moreover, the theoretical correlation between the hydrodynamic force and the body geometry allows us to control the inverse problem, and the shape associated to a constant slamming force is determined.