In this study, miscible displacement experiments were carried out in saturated soil columns for Cu and Zn. The studies were conducted in glass columns of length 50 cm and diameter of 4 cm. The column is specifically designed to study the shifting of mass transfer zones in adsorption process. It has a unique sampling port at every 7 cm vertically which are equipped with the sampling device. Agricultural soil sample from paddy fields of Udupi district, Karnataka, was used for the experiment. Breakthrough curves for the different heavy metals were plotted. Two kinetic models, Thomas model and Yoon-Nelson were applied to the data obtained from the column experiment using linear regression. Results showed that both kinetic models were found suitable for the breakthrough curves of studied heavy metals and hence can be used to analyse the performance of the column bed. The values of coefficient of determination (R2) are in the range of 0.87 to 0.97 for both models. The adsorption was in the order Zn > Cu, indicating that Zn adsorbs onto the soil samples readily than Cu.