We present an efficient technique for the solution of free surface flow problems using level set and a parallel edge-based finite elementmethod. An unstructured semi-explicit solution scheme is proposed. A custom data structure, obtained by blending node-based and edge-based approaches is presented so to allow a good parallel performance. In addition to standard velocity extrapolation (for the convection of the level set function), an explicit extrapolation of the pressure field is performed in order to impose both the pressure boundary condition and the volume conservation. The latter is also improved with a modification of the divergence free constrain. The method is shown to allow an efficient solution of both simple benchmark cases and complex industrial examples.