In the present paper we discuss the computation of eigenmodes of closed water basins with focus on Lake Constance. As model we use the shallow-water equations for a one-layered closed basin with variable bottom shape. We discretize the equations with linear finite elements on a specially constructed grid. As solver we use the standard multigrid method for eigenvalue problems coupled with a robust ILU smoother, which is supported by a particular numbering strategy. The resulting method, the convergence of which is analyzed thoroughly, is very efficient, allowing the solution of the Lake Constance problem on an Apple Macintosh in reasonable time. The results are compared with several existing ones.