A heat exchanger element for a Stirling cycle refrigerator is produced by integrally forming an annular corrugate fin that is produced by forming a sheet material, corrugated so as to have a large number of grooves, into a cylindrical shape with the grooves parallel to an axis of the cylindrical shape and an inner ring-shaped member that is placed in contact with the inner periphery of the annular corrugate fin. A heat rejector or heat absorber for a Stirling cycle refrigerator is produced by inserting this heat exchanger element into the hollow portion of a tubular body.