A two-dimensional numerical model has been developed to simulate the electrokinetic remediation of soils contaminated with heavy metals and has been validated using laboratory experiments performed with a copper spiked kaolin. The model divides the soil into compartments in a Cartesian grid and a non-conductivity barrier encloses the considered area. Basically, it consists in two main parts clearly distinguishable. The first part describes the electromigration phenomenon in the soil, which is represented by a set of electric resistors, following the Cartesian grid and using Kirchoff's laws of electricity to calculate the voltage drop distribution in the considered area. The second part describes the chemical equilibrium process between the heavy metal and the soil, assuming local equilibrium conditions within the compartments. A good agreement was obtained between the lab scale experimental assays and the model predictions. The model has also been used to examine the effect of the electrolyte neutralization within the scope of the acid-enhanced electrokinetic method. These simulations have foreseen problems related with the system evolution, which would not arise under one-dimensional geometries and are due to the changes of the potential distribution in the two-dimensional arrangement where some kind of short circuit arises, ultimately leading to a decrease of the system efficiency.