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A two-fluid solver has been developed for flow problems with both moving solid bodies and free surfaces. The underlying scheme is based on the solution of the incompressible Navier–Stokes equations for a variable density fluid system with a free surface. The cut cell method is used for tracking moving solid boundaries across a stationary background Cartesian grid. The computational domain encompasses fully both fluid regions and the fluid interface is treated as a contact discontinuity in the density field, which is captured automatically without special provision as part of the numerical solution using a time-accurate artificial compressibility method and high resolution Godunov-type scheme. A pressure-splitting algorithm is proposed for the accurate treatment of the normal pressure gradient at the interface in the presence of a gravity term. The Cartesian cut cell technique provides a highly efficient and fully automated process for generating body fitted meshes, which is particularly useful for moving boundary problems. Several test cases have been calculated using the present approach including a moving paddle as a wave generator and the initial stages of entry into still water of rigid wedges. The results compare well with other theoretical results and experimental data. Finally, test cases involving the entry into water and subsequent total immersion of a two-dimensional rigid wedge-shaped body as well as the inverse problem of wedge egress have been calculated to demonstrate the ability of the current method to tackle more general two fluid flows with interface break-up, reconnection, entrapment of one fluid into the other, as well as handling moving bodies of complex geometry.