Abstract: This article presents a novel nonreflective boundary condition for the free surface incompressible Euler and Navier-Stokes equations. Boundaries of this type are very useful when, for example, simulating water flow around a ship moving over a wide ocean. Normally waves generated by the ship will reflect off of the boundaries of the simulation domain and as these reflected waves return towards the ship they will cause undesired interference patterns. By employing a Perfectly Matched Layer (PML) approach we have derived a boundary condition that absorbs incoming waves and thus efficiently prevents these undesired wave reflections. To solve the resulting boundary equations we present a fast and stable algorithm based on the stable fluids approach. Through numerical experiments we then show that our boundaries are significantly more effective than simpler reflection preventing techniques. We also provide a thorough analysis of the parameters involved in our boundary formulation and show how they effect wave absorption efficiency.