A numerical analysis technique for free surface flow problems by FEM is presented. The VOF (Volume of Fluid) method is employed in order to represent the free surface by Eularian mesh. FEM with the VOF method mentioned here is convenient to simulate the large deformation of the free surface without re-meshing. The convective equation of VOF is solved by a fully implicit scheme, thus simulating shapes and locations of the free surfaces accurately. Numerical calculations were carried out for the breakdown flow of a dam and the mold filling simulation in die casting and these results were examined in comparison with experimental results and calculation results in the references.