The effect of water saturation on the transport of a conservative, nonreactive solute pulse by quasi steady state and transient flows in a vertical cross section of a hypothetical, yet realistic heterogeneous, partially saturated soil has been analyzed here by a series of numerical experiments. Mean water saturation in the flow domain was controlled by predetermined capillary pressure head at the entry zone, or by predetermined time interval between successive water applications. Analyses of the simulation results show that under both quasi steady state and transient flow regimes, lower degree of water saturation enhances solute spreading, in qualitative agreement with the results of Lagrangian-stochastic analyses of vadose-zone transport . The pattern of the velocity field, and, consequently, the spreading of the solute body, were affected considerably by the boundary conditions imposed on the flow at the entry zone. In the case of the quasi steady state flows under predetermined capillary pressure heat at the inlet zone, the flow was essentially unidirectional vertical, with slight local deviations and, consequently, solute spreading took place mainly in the longitudinal direction. In the case of transient flows under periodic influx, the flow pattern was more complicated, essentially two dimensional, thereby restricting the longitudinal spreading of the solute plume and enhancing its transverse spreading. In the comparison paper (Russo et al., this issue), integrated measures of the simulated solute plumes are compared with their predicted values, based on the first-order Lagrangian-stochastic analysis.