This paper continues the development of boundary integral equation technique for solving stochastic groundwater flow problems. The case of aquifers under deterministic hydraulic conductivity, but subject to random boundary condition and domain recharge has been investigated in an earlier paper under the assumption of steady state governing equation. In the current paper the governing equation is transient, but the temporal variation of second-order statistical moments is assumed to be weakly stationary. Several examples of fundamental importance to the understanding of stochastic process are examined both by the analytical and by the numerical (boundary element) techniques. ¿ American Geophysical Union 1993