A 1-D model for the flushing of metal contaminated soils with extracting aqueous solutions is presented. Previous experimental results of the flushing of carbonatic soil contaminated with lead with EDTA solutions showed the formation of channels of preferential flow as well as substantial rebounds in effluent lead concentration after periods of no pumping, indicating an important kinetic limitation for lead removal. This limitation is associated with the presence of a stagnant aqueous phase in addition to the mobile aqueous phase running through the channels. The model assumes an initial homogeneous distribution of lead in the soil, mainly present as small spheres of a solid carbonate which must dissolve. If the spheres are far from the channels, after solution the lead must diffuse through the stagnant aqueous phase until it reaches the channels and is washed out of the column. The model is able to simulate the rebound curves as well as the effluent concentration during the course of the operation. The importance of the way the channels arise is established by sensitivity studios performed for different mechanisms of the solution circulation and the formation of channels. More experimental results are needed to discriminate which of the alternatives studied is operative.