The classical problems of steady-state flow under a sluice gate and over a spillway are solved by the boundary integral equation method. In both cases an iterative methods is used to adjust the free-surface profiles until they satisfy both the kinematic and dynamic boundary conditions. In the case of sluice gate flow, a point by point adjustment method is used which quickly converges to the correct solution within three to six iterations. The results closely check previous, less efficient calculations. Some of the variation is past experimental results is explained by calculations in which the geometry of the gate is altered slightly near the tip. Even a small change from the ideal geometry can have a major effect on the contraction coefficient. Flow over a spillway is a more difficult problem due to poor convergence properties in the free-surface profile behind the spillway crest.