The present study aims to simulate and compare various approaches for modeling the equilibrium and non-equilibrium water flow and potassium transport. Laboratory column experiments were done using polyvinyl chloride columns (PVC), 65 cm long and 19 cm diameter (283.5 cm2 surface area) with closed bottoms. The columns were hand-packed with air dried sandy loam soil for length of 60 cm at constant bulk density by gently tapping (1.417 Mgcm-3). Potassium solution with three concentrations i.e. 12.5, 100 and 200 mg/l was added at constant rate using Mariotte bottle. The solute drained from the bottom of each column was collected in glass bottle, and then volume and K concentration were measured with time.Also, soluble and sorbed potassium in soil columns were determined for 5 cm segments. The results indicating that the predicted data according to the equilibrium and non-equilibrium transport models showed a symmetrically distribution of soluble potassium for medium and high K input concentration. For low K input concentration, the results showed a symmetrically distribution for OSM (one-site sorption model) and DPTS (dual permeability with two-site sorption model). Also, a symmetrically distribution was found with DPM (dual porosity model) and TSM (two –site sorption model). The K distribution of EQ (equilibrium model) has a high values than other four models. A general conclusion of the present study is that a model's success or failure to represent the flow and transport processes internal to the transport domain should not be judged solely by the response prediction at a single outlet point. Therefore, we need more experimental data and more comprehensive studies of many soil types to evaluate how much and what type of information is required to fully parameterize selected non-equilibrium models of water and solute transport.