A method of extracting an analyte from a sample is described. The sample is added to a sample container. A liquid solvent and a gas are added into the sample container. The addition of the gas is controlled to establish an elevated pressure within the sample container. The liquid solvent is heated to an elevated temperature that is below the boiling temperature of the liquid solvent at the elevated pressure. A type of gas is used that does not transition to a supercritical fluid at the elevated temperature and pressure used in the extraction process. The analyte can dissolve from the solid sample into the liquid solvent. Next, at least a portion of the liquid solvent containing the dissolved analyte can be removed from the sample container for subsequent analysis.