The cubic spline integration scheme has been successfully applied for the first time to obtain solutions for the two-dimensional shallow water wave and transport equations. Its principal advantages are its high accuracy, low computational cost, and flexibility of application. The study quantitatively analyzed and predicted the variation in time and space of a solid pollutant in water environment. The infiltration, adsorption, solubility, advection, and diffusion related factors at different spatial and temporal scales were taken into consideration in the model. Experiments were conducted in this study to examine the capabilities of the cubic spline scheme. The correspondence between the numerical results and the experimental data was fair. The results were also compared with the numerical results obtained using finite difference schemes with good agreement.