Potential theory is used to analyze free-surface, irrotational flow over spillways of finite height. Numerical values were obtained for free-surface coordinates, pressures on the surface of the spillway, and discharge coefficients for three separate spillway shapes. The spillways considered included (a) one corresponding to the shape of the nappe produced by flow over a ventilated, sharp-crested weir, (b) one corresponding to the shape of the nappe produced by flow over a ventilated, sharp-crested weir with nagative pressure head beneath the nappe equal to one-half the head on the weir and (c) one having vertical upstream face, a cylindrical crest, and a downstream tangent inclined 30○ from the vertical. Because flows of several heads were analyzed for each spillway, certain conclusions were drawn relative to spillway operation under high heads.