In order to better management of contaminants in porous media, it is essential to recognize their transport behavior using appropriate models. In this research, Convection-Dispersion Equation (CDE) and Mobile-ImMobile (MIM), as physical equilibrium and non-equilibrium models, respectively, were used to simulate the bromide transport (as a conservative contaminant) through undisturbed and saturated clay loam and sandy loam soil columns (diameter of 10 and height of 40 cm). To simulate the transport, CXTFIT2.1 software, in which the CDE and the MIM models are included, was used. The values of mass transfer coefficient (ω<100) and mobile water fraction (β<1) as an indicator for determining the equilibrium and non-equilibrium indicated that bromide transport behavior within these columns was anomalous or non-Fickian transport. Hence, non-equilibrium and the MIM model are suitable and more efficient than the Fickian-based CDE. The fitted breakthrough curves (BTCs) and the larger determination coefficient (R2) and the smaller Root Mean Square Error (RMSE) values of the MIM model compared to those of the CDE confirmed the effectiveness of the MIM model in simulating bromide transport in the clay loam and sandy loam soil columns.