A comparison of linear and non-linear regression method for predicting the optimum isotherm was made using the experimental adsorption equilibrium data of Cu(II) onto treated Martil sand (TMS). For this, six error analysis methods were used: the coefficient of determination r(2), the sum of the squares of the errors, the sum of the absolute errors, the average relative error, the hybrid fractional error function and the Marquardt's percent standard deviation. The error values indicated that non-linear method is a better way to obtain the isotherm parameters describing the Cu(II) adsorption onto TMS. The comparison between different models such as Langmuir, Freundlich, Dubinin-Radushkevich, Temkin, Redlich Peterson, Koble-Corrigan and Fritz-Schlunder showed that Fritz-Schlunder model was more suitable to describe the equilibrium data. Based on this result and in order to optimize the equilibrium model results for more accurate parameters values, the Fritz-Schlunder equation was modified and called modified Fritz-Schlunder model. As a comparison of such developed modified model to existing mentioned ones, the results showed that the adsorption equilibrium of Cu(II) onto TMS was better described by the modified Fritz-Schlunder model than by others. (C) 2016 Elsevier B.V. All rights reserved.