An extraction method for preparing samples for analytical analysis is disclosed. The method includes the steps of placing a sample matrix containing one or more analytes in a heat conductive sample cup, positioning the heat conductive sample cup in a pressure-resistant reaction chamber, dispensing solvent into the heat conductive sample cup, dispersing the solvent and the sample matrix in the sample cup in the reaction chamber, heating the sample matrix and the extraction solvent in the heat conductive sample cup in the reaction chamber to a temperature at which the dispensed solvent generates an above-atmospheric pressure, and releasing the extraction solvent extract from the sample cup at atmospheric pressure.