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In this paper, a method for the treatment of the swelling of expansive soil is numerically simulated. The method is simply based on the embedment of a geogrid (or a geomesh) in the soil. The geogrid is extended continuously inside the volume of the soil where the swell is needed to be controlled and orientated towards the direction of the swell. Soils with different swelling potentials are employed: bentonite base-Na and bentonite base-Ca samples in addition to kaolinite mixed with bentonite. A numerical analysis was carried out by the finite element method to study the swelling soil's behavior and investigate the distribution of the stresses and pore water pressures around the geocells beneath the shallow footings. The ABAQUS computer program was used as a finite element tool, and the soil is represented by the modified Drucker-Prager/cap model. The geogrid surrounding the geocell is assumed to be a linear elastic material throughout the analysis. The soil properties used in the modeling were experimentally obtained. It is concluded that the degree of saturation and the matric suction (the negative pore water pressure) decrease as the angle of friction of the geocell column material increases due to the activity of the sand fill in the dissipation of the pore water pressure and the acceleration of the drainage through its function as a drain. When the plasticity index and the active depth (the active zone is considered to be equal to the overall depth of the clay model) increase, the axial movement (swelling movement) and matric suction, as a result of the increase in the axial forces, vary between this maximum value at the top of the layer and the minimum value in the last third of the active depth and then return to a consolidation at the end of the depth layer.