Soil erosion due to head cut development and migration can devastate agricultural lands, yet current prediction technology does not address this important erosion process. Here an analytical model of this erosional phenomenon is presented. Realistic, physically based approximations to the laws governing mass, momentum, and energy transfer in the neighborhood of the scour hole result in closed-form predictive algorithms for the magnitude of the plunge pool erosion and the rate of head cut migration. The model introduces a special treatment of nonventilated overfall conditions, is limited to homogeneous, unbounded soil layers, and is validated by available experimental measurements.