Modeling of the supercritical fluid extraction of solid materials is an important aspect in order to understand and predict the process. A comparison of two empirical models, two semi-empirical models and two mechanistic models is performed using calibration of single experiments. It is concluded that the best fit is obtained using a simple empirical expression. Furthermore, single calibrations did not generate reliable parameters with physical meaning and a methodology is proposed for inverse modeling with complete calibration using several experiments. The experimental dataset contained 29 extractions of lipids from crushed linseeds with varying temperatures, pressures and flow rates. A general rate model and a proposed extension of the hot ball model were evaluated for this purpose. The methodology includes data acquisition, model structure estimation, model calibration and a cross-validation. In general, it was found that the solubility model of Sovova outperformed the other evaluated correlations, and for the general rate model the Toth partition isotherm was also found in the top model structures. However, no generalization could be made regarding the correlations describing the Nernst diffusion layer and diffusivity. (C) 2016 Elsevier B.V. All rights reserved.