A continuous-flow extraction system and method for extracting oil from oil-bearing plant parts, or biomass, with liquid-phase hydrocarbon solvent in a continuous process, providing more than one extraction vessel so that one or more extraction vessels can be cleared of exhausted biomass and reloaded with biomass, while another one or more extraction vessels are undergoing the extraction process, optionally providing a de-waxer for use when needed, providing a primary jacketed separator vessel for flashing hydrocarbon solvent to a vapor phase and precipitating and collecting liquid plant extract, providing at least one secondary jacketed separator vessel for purification and refinement of vapor-phase hydrocarbon solvent and providing for re-liquefication of the solvent for the purpose of re-circulating and reusing the solvent, and providing for the heating, cooling, and pumping necessary to carry out the various steps.