The transport of solutes through porous media where chemicals undergo adsorption or change process on the surface of the porous materials has been a subject of research over the years. Use of pesticides has resulted in production of diverse quantity and quality for the market. Disposal of excess material has also become an acute problem. The concept of adsorption is essential in determining the movement pattern of pesticides in soil in order to assess the effect of migrating chemicals from their disposal sites on the quality of ground water. In this paper, we derive a two dimensional equation accounting for both lateral and axial pesticide flow in a porous media by convective- dispersive transport with steady state water flow. The model is derived from the first principle and solved using Alternation-Direct-Implicit (ADI) method.