In this, the second of two papers concerning the stochastic description of solute transport under unsteady flow conditions, we show how the ensemble-averaged solute transport equation derived in the companion paper <Wood and Kavvas, this issue> can be solved. A two-dimensional analysis is conducted under conditions that are representative of the Borden aquifer, and a solution to the ensemble-averaged solute transport equation is found numerically. The analytical model suggested by Dagan et al. <1996> is adopted for the velocity field mean and Lagrangian covariance functions. The numerical solution provides the ensemble-averaged concentration field under transient flow conditions; from this concentration field the first- and second-order moments of the ensemble-averaged solute plume are calculated. The ensemble-averaged plume moments compare favorably with the moments calculated using the approach of Dagan et al. <1996>, with the plume moments from a Monte Carlo analysis, and with plume moments measured in the field. In our approach the Darcy-scale dispersion is not neglected, and it is shown that this dispersion term has a small but significant influence on the resulting solutions. ¿ 1999 American Geophysical Union