Technical Abstract: The ability to predict the sediment trapping efficiency of a impoundment is an integral part of the erosion control planning process. The Water Erosion Prediction Project Surface Impoundment Element (WEPPSIE) was developed to add impoundment analysis capability to the existing Water Erosion Prediction Project (WEPP) runoff and sediment yield model. This work describes the hydraulic analysis portion of WEPPSIE. To perform the necessary computations in a timely manner, continuous algebraic forms of the stage-discharge and stage-area relationships, as opposed to forms requiring interpolated or iterative solutions, were desirable. Development of the algebraic approximations of the conventional stage-discharge computation methods for perforated risers, open channel spillway, and rockfill check dams is described here. The performance of the algorithms given a variety of structure geometries was assessed by comparing their output with results obtained using the conventional methods. The algebraic approximations reproduced the conventional methodologies well in most cases.