We present a discontinuous Galerkin method on a fully unstructured grid for the modeling of unsteady incompressible fluid flows with free surfaces. The surface is modeled by embedding and represented by a level set. We discuss the discretization of the flow equations and the level set equation as well a various ways of advancing the equations in time using velocity projection techniques. The efficacy of the method for the representation of the level set and its reinitialization is discussed and several numerical tests confirm the robustness and versatility of the proposed scheme. (c) 2005 Elsevier B.V. All rights reserved.