Abstract: Methods for extracting metalloid and metal species from a solid or liquid material by exposing the material to a fluid solvent, particularly supercritical CO.sub.2, and a chelating agent are described. The chelating agent forms a chelate with the species, the chelate being soluble in the fluid to allow removal of the species from the material. In preferred embodiments the extraction solvent is supercritical CO.sub.2 and the chelating agent comprises an organophosphorous chelating agent, particularly sulfur-containing organophosphorous chelating agents, including mixtures of chelating agents. Examples of chelating agents include monothiophosphinic acid, di-thiophosphinic acid, phosphine sulfite, phosphorothioic acid, and mixtures thereof. The method provides an environmentally benign process for removing metal and metalloids from industrial waste solutions, particularly acidic solutions.