An analytical transport‐model was developed to simulate the propagation of a contaminant in one‐ and two‐dimensional transient flow in groundwater. It is proved that the distribution of concentration at a given time and for a given discharge is identical to that obtained for a different discharge if the volumetric flux of water is the same in the two cases. The results of simulations have been compared with results obtained using the MT3DMS numerical model. There is good agreement when the calculated concentrations are flux‐weighted concentrations. On the other hand, there is a notable divergence when the resident mode is considered. Resident mode concentrations express the mass per unit volume whereas flux mode concentrations express the ratio of mass flux to fluid flux. The solutions presented in this paper can thus be a useful alternative to code MT3DMS when the objective is to simulate concentrations in transient flow according to a resident mode. Copyright © 2008 John Wiley & Sons, Ltd.