The precursor effect occurs when a dilute influent solution displaces a high-concentration resident solution. Some of the influent material is transported with the resident solution and appears around 1 pore volume in the breakthrough curve. A numerical solution of the mathematical model of the precursor effect is used to elaborate our understanding of precursor formation and improve and extend the use of an existing analytical approximation. The numerical results lead to a simple method of estimating the amount of material making up the precursor, and the concentration of material behind the precursor. A comparison of numerical results with laboratory data shows good agreement, but indicates that experimental conditions will then lead to greater dispersion of the precursor than is predicted by the model.