A hospital drug distribution system for efficiently distributing solid medicinal units to hundreds of patients comprises subsystems for placing trays on a conveyor, placing cups thereon, labeling the cups, conveying the cups under drug tubes, sealing the cups, unloading the trays, and coordinating the overall activities of the system. Medicinal units are stored in long, thin vertical tubes positioned side-by-side, and are dispensed by valves disposed at the bottom of each tube. The rows of tubes are suspended over a conveying means transporting individual medication cups. The cups are arranged on trays on the conveying means in single file. The computer-controlled conveying means proceeds in a step-and-stop fashion, such that each cup stops briefly beneath each drug tube. When a cup completes its journey beneath the drug tubes, it contains the drugs needed by the patient to which it is assigned. Barcode readers at each valve scan the approaching cup to determine if drugs from the attached tube should be dispensed into it. The system is modular, as additional modules including multiple tubes can be added or removed as needed. When a tube becomes empty, it is discarded or sent to a drug refilling center for restocking. The hospital orders from the refilling center all needed tubes daily, preferably automatically over a computer network by a computer that tracks drug inventory levels. Replacement tubes are delivered overnight or within hours, depending upon the need. The system preferably operates in manual mode for special one-time orders.