Analytical models of saltwater intrusion in coastal aquifers of finite size are developed and utilized in an optimization methodology for determining the optimal pumping rates. The models are based on the sharp interface approximation and the Ghyben-Herzberg relation. The governing equations are expressed in terms of a single potential and are solved analytically using the method of images to account for the aquifer boundaries. The analytical models consider ambient flow and surface recharge. The results are compared to numerical simulations indicating a good match as the number of images is increased. The objective of optimization is to maximize the total pumping from the aquifer and a set of constraints protect the wells from saltwater intrusion. The constraints are expressed using the analytical saltwater intrusion models. Two different constraint formulations are investigated. The toe constraint formulation protects the wells from saltwater intrusion by not allowing the toe of the interface to reach the wells. This formulation results in a nonlinear optimization problem which is solved using sequential quadratic programming (SQP). The potential constraint formulation, on the other hand, protects the wells by maintaining a potential at the wells larger than the toe potential. This formulation results in a linear optimization problem which is solved using the Simplex method. Several simulation runs indicate that the optimal solution is very sensitive to variations of recharge rates, hydraulic conductivity heterogeneities, etc. The linear programming formulation, besides being computationally simpler, provides a safer solution than the nonlinear formulation.