In this paper an algorithm based on finite element methods is presented to value an American type of swing contracts with multiple exercise rights. Thereby the reduction of multiple stopping time problems to a cascade of single stopping time problems is utilized. The numerical results obtained with the proposed algorithm show a smooth and stable behavior. This allows an interpretation of the swing options’ optimal exercise boundaries and an analysis of the dependence of swing option prices on the initial spot prices. A comparison of the finite element algorithm to Monte Carlo and lattice methods demonstrates the strengths of the proposed numerical algorithm.