The removal of dye from industrial wastewater is one of the most important subjects in water pollution regulation. Successive adsorption/desorption cycles of a basic dye, methylene blue, on internal almond shell, olive stone and rye straw were investigated by using fixed bed column experiments to study the adsorption capacity to remove the MB and adsorbents regeneration efficiency. The adsorption breakthrough curves were predicted by the Thomas model, Yoon Nelson model, and Wolborska model and modified dose-response model by using nonlinear regressive analysis. The adsorption capacity values obtained by this model are compared with the experimental capacity, noting an error of 16%, 27.8% and 18.9% for IAS, OS and RS respectively, but these errors are minimized in the second cycle to 22.98% and 6.06% for OS and RS respectively. The results show that the modified dose response model is more suitable for the description of breakthrough curves for three adsorbents only in the first cycle. The IAS presents the highest adsorption capacity and the best regeneration efficiency. Conversely, the RS presents lower adsorption capacity, whereas is not the hardest to regenerate.