A mass preserving finite element formulation of the Level Set method is presented. The formulation is based on the discontinuous representation of the level set function and involves the Runge-Kutta Discontinuous Galerkin (RKDG) finite element method. The resulting formulation has the flexibility of treating a complicated geometry by using arbitrary triangulation. The performance of the scheme is demonstrated on a number of two-dimensional re-distance and coupled advection-redistance problems. The results indicate that the RKDG finite element formulation provides accurate solutions of the Level Set problem and has great potential in fluid dynamics applications.