A container unit for a drug is composed of a container, which is formed of a cylindrical drug-solution-containing portion and a drug-solution-filling neck portion, and a rubber closure for sealing the drug-solution-filling neck portion. The rubber closure comprises a disk-shaped head portion and a substantially cylindrical leg portion arranged on a lower wall of the head portion. The container is provided with a flat surface formed on a side of its inner wall at a boundary between the drug-solution-containing portion and the drug-solution-filling neck portion such that a lower end wall of the leg portion of the rubber closure can be brought into close contact with the flat surface, and at least a side wall of the drug-solution-containing portion forms a cornerless, rounded surface on a side where a drug solution is to be contained. When the drug-solution-filling neck portion has been sealed with the rubber closure, the lower end wall of the leg portion and the flat surface of the container are maintained in close contact with each other without any protrusion of an inner circumferential edge of the lower end wall into an interior of the container beyond an inner circumferential edge of the flat surface.