This paper compares the efficiency of seventeen different methods for the solution of the simultaneous nonlinear finite difference approximating equations for groundwater flow in a watertable aquifer in three dimensions. Solution methods include those of Newton, Picard, and generalized linear methods. The Newton and Picard iteration methods were implemented by making use of several different linear methods including successive overrelaxation, the strongly implicit procedure, and eight different preconditioned conjugate gradient methods. The best methods were found to be those using Picard iteration implemented with the preconditioned conjugate gradient method.