In this study, La3+, Ge3+ and Sm3+ were removed from a solid matrix using supercritical CO2 which contained bis(2,4,4-trimethylpentyl)dithiophosphinic acid (Cyanex 301) as a chelating agent and tributylphosphate (TBP) as a co-extractant. The fractional factorial design, 2(5-1), was employed to optimize the SFE of these ions from spiked filter paper matrices. Effect of five experimental factors: amount of Cyanex 301, flow rate, temperature, pressure and amount of TBP and each factor at two levels on the SFE of these ions were studied and optimized. The results showed that these ions could be quantitatively extracted from the solid matrix at amount of Cyanex 301 of 0.14g, flow rate of 4 ml min(-1), 313 K, 250 bar and amount of TBP of 30 mu l. Finally, by employing a regression analysis a model was proposed. Results showed that obtained recoveries are similar to those predicted by the model. (C) 2010 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.