Shape optimization problems in fluid dynamics governed by the free surfaceflows are considered. Such problems are inspired by the process of continuouscasting of steel where optimization of large vortex structures in different metallurgicalreactors is of paramount importance to ensure good quality output. Thepseudo-transient approach is used as solution strategy for solving the free surfaceproblem. Design sensitivities involving different cost functionals are derived usinga formal Lagrangian framework. Numerical results are presented which indicatethe success of the proposed algorithm for solving this free surface shape optimizationproblem.