The one-dimensional groundwater flow equations are coupled with the St. Venant equations to simulate the flow resulting from a sudden removal of a dam over an initially dry downstream bed. The St. Venant equations are solved using a Petrov-Galerkin finite element scheme, while the groundwater flow equations are solved using the Bubnov-Galerkin finite element scheme. The comparison of the computed water surface and discharge per unit width profiles with the corresponding analytical solutions, for a dambreak over frictionless horizontal bed, show that the model possesses excellent phase accuracy, for both positive and negative waves, and can predict the discharge distribution accurately. Also, the computed water surface profiles are compared with the available measured data for the dambreak flows over smooth and rough surfaces of horizontal and sloping channels. In addition, the results obtained from only the St. Venant equations with minimum depth criteria are presented for comparison with the above model.