In order to accurately predict contaminant transport in soil, the processes and factors affecting on this phenomenon should be identified, measured and mathematically defined. The amount of initial concentration and input flux (release rate) of contaminant are among these factors. In this study, transport of the heavy metal Zn in saturated sandy soil columns was simulated and evaluated by the equilibrium and non-equilibrium models. Also, the effects of initial concentration and input flux on Zn transport were investigated by choosing three levels of initial concentration (10, 50 and 100 mg L⁻¹) and input flux of 0.5K_s, 1K_s and 1.5K_s. The results showed that for simulating the Zn transport in the columns containing the initial concentration of 50 and 100 mg L⁻¹, the equilibrium model and for the columns with the initial concentration of 10 mg L⁻¹, the physical non-equilibrium mobile–immobile model had a better performance. The initial concentration and the adsorption (retardation factor) were inversely and linearly related to each other; while the input flux was directly and linearly proportional to the adsorption. The increase in initial concentration of Zn from 10 to 50 and from 50 to 100 mg L⁻¹ and under the input flux of 1K_s decreased the amount of Zn adsorption by 13.38% and 57.71%, respectively. The increase in the input flux from 0.5 to 1K_s and from 1 to 1.5K_s and under an initial concentration of 100 mg L⁻¹ resulted in an increase of 34.79% and 17.88%, respectively, in the amount of Zn adsorption in the soil columns.