An apparatus wherein assayed specimens can be transferred in any order to a specimen-container housing rack automatically and very efficiently, without any restrictions whatsoever on the order in which the specimen containers are placed in the specimen-container racks and assayed, even if different types of specimen vessel are present. This is accomplished in a specimen-container transfer apparatus having: a conveyor unit for transporting specimen-container racks; a specimen-container ID reader for reading the specimen-container identification numbers of the specimen-container racks transported by the conveyor unit; a specimen-container housing-rack table for setting up specimen-container housing racks for housing specimen containers; a specimen-container transfer mechanism for taking specimen containers out of a specimen-container rack and putting them in a specimen-container housing rack; and a control unit for controlling the order in which the specimen containers are put into the specimen-container housing rack.