This paper continues the development of boundary integral equation tec
hnique for solving stochastic groundwater flow problems. The case of a
quifers under deterministic hydraulic conductivity, but subject to ran
dom 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 te
mporal variation of second-order statistical moments is assumed to be
weakly stationary. Several examples of fundamental importance to the u
nderstanding of stochastic process are examined both by the analytical
and by the numerical (boundary element) techniques.