A model has been developed for use in determining the optimal dimensions of stilling basins for overflow dam spillways and their appurtenances that minimize cost and satisfy hydraulic performance. The decision variables which are the width and elevation of the stilling basins are determined such that the hydraulic performance is satisfied for a wide range of possible spillway discharges. The model is based upon an optimization procedure with two phases. The first phase is used to optimize the hydraulic performance of a stilling basin and the second phase is to use the first phase results to minimize the cost satisfying required basin performance. Both phases are based upon a gradient search technique. Application of the optimization model was made using data for the spillway and stilling basin designs for three dams in Texas.