A mathematical model is evaluated to describe cesium reaction and transport in a soil. The implicit finite difference method using quasilinearization technique is applied to solve the parabolic partial differential equation. This equation is a combination of the dispersion, convective transport, and sorption, where the sorption models are expressed as two nonlinear reaction equations (two-stage model). Under the condition of steady state soil water flow, this model describes the effluent concentration distributions of cesium solutions both adsorption and desorption; neither of which are adequately described using a single adsorption model. This model is flexible and may be adapted to incorporate the various transformation mechanisms of other radionuclides sorption on a soil, and this numerical approximation appears to have broad and practical utility.