The present invention relates to a process for producing hydrogen and for separating carbon dioxide from synthesis gas using a physical absorption medium. The process comprises the steps where the synthesis gas and the absorption medium are cooled; carbon dioxide is removed from the cooled synthesis gas via the cooled absorption medium in a physical absorption step at elevated pressure; laden absorption medium is treated in a plurality of flash stages, wherein co-absorbed carbon monoxide, hydrogen and carbon dioxide are separately removed from the laden absorption medium; hydrogen is separated from synthesis gas freed of carbon dioxide in a physical separation step, wherein hydrogen as product gas and an offgas comprising hydrogen, carbon monoxide and carbon dioxide are obtained; product gas hydrogen and carbon dioxide are discharged from the process. The invention further relates to a plant for performing the process.