A simple lumped parameter stochastic model for optimal water management in a stream‐connected aquifer system is examined. The physical system is represented by a linear reservoir model, and a conditional probability approach is used to estimate the effect of parameter variability. A drawdown correction is used to incorporate the local drawdown of the wells and is a crucial part of the model. A management analysis is carried out by using a linear decision rule to minimize the expected value of the discounted costs with appropriate chance constraints, and the resulting nonlinear optimization problem is solved iteratively by using a standard linear programing package. In order to evaluate the limitations of the lumped parameter model in a management context, the results of the management technique are compared with results from Maddock (1974) who used a distributed representation of the aquifer. The conclusions of this analysis indicate that stochastic effects are not very important in arriving at an operating policy but are important in determining the expected cos