Groundwater flow through bounded rectangular aquifers is analyzed in a stochastic framework. New analytical expressions of the head covariance (and variance) and the log transmissivity head cross covariance are derived for the simplified first-order problem. Effects of different boundary conditions, the aquifer size, and the log transmissivity correlation scale upon head moments are studied. The results are compared to analytical half-plane solutions, demonstrating significant differences in several cases. Finally, the problem is solved numerically using the Monte Carlo simulation method. The realizations of the log transmissivity field are generated in two different ways. Through comparisons with the analytical results the accuracy of the numerical methods is shown to be excellent. ¿ American Geophysical Union 1995