A container includes a casing defining an annular chamber for a volume of thread or wire pre-wound into coils to accommodate therein without becoming tangled, and a cover detachably closed onto the casing. A clearance exists between an upper peripheral edge of the casing and a lower peripheral edge of the cover when the cover and the casing are closed, allowing a free end of the thread or wire in the annular chamber to locate outside the container via the clearance. Therefore, the thread or wire in the container could be easily accessed and pulled outward at the free end for use without the need of opening the cover. The container could be refilled with a new thread or wire and therefore could be repeatedly used.