PROBLEM TO BE SOLVED: To provide a cap structure such that an opening part and a seal material of a container sealed with the seal material such as a rubber stopper, are covered with a cap, and a part of the cap is cut off to expose the seal material.SOLUTION: A cap structure has one or a plurality of protrusions which protrude downward on a bottom part of a disk part or a cutting protrusion part and at a position radially apart from an axis line of the cutting protrusion part, the protrusions are each fitted on a seal member while pressing the seal member in a repulsive manner, and a thin part is formed at the upper part of an annular guide wall surface which surrounds an outer edge part of the disk part when the disk part is displaced downward and cut off, and the guide wall surface is set to be longer than a length by which the disk part is pressed down when the disk part is cut off.