Groundwater management models are often applied to problems in which the aquifer state is a mildly nonlinear function of managed stresses. The use of the successive linear programming algorithm to solve such problems is examined. The algorithm solves a series of linear programs, each assembled using a response matrix. At each iteration perturbation from the most recent value of the managed stresses is used to estimate response coefficients. Iterations continue until a convergence criterion is met. The algorithm is tested on a water supply problem in Antelope Valley, Calif. where large volumes of water are injected and extracted each year producing a significant nonlinear response in the unconfined aquifer. The algorithm is shown to perform well under a variety of settings.