In a multi-stage cold accumulation type refrigerator including a compressor disposed at an ordinary temperature, a helium gas as a common operating fluid to be compressed by the compressor, and one or more expansion chambers and cold accumulators of different temperature levels; a cold accumulating member of the cold accumulators is formed of an alloy or compound containing a rare earth metal, so that the efficiency of the refrigerator can be improved. Further, a heat generation quantity due to sliding resistance of a seal is set to be smaller than a theoretical generated refrigeration quantity to be obtained on the assumption of isothermal expansion in the expansion chambers, so that the refrigerating capacity can be improved. The refrigerator is applied to a cooling device for cooling a superconducting magnet, SQUID, superconducting computer, infrared telescope, etc.