Solute transport through porous media is usually described by well-established conventional transport models with the ability to account for advection, dispersion, and sorption. In this study, we further extend our previous one-dimensional model for solute transport in an unsaturated porous medium to two dimensions. The present model is based on a small-strain approach. The proposed model is validated with previous work. Both homogeneous landfill and pointed landfill conditions are considered. A detailed parametric study shows the differences between the present model and previous one-dimensional model.