A socket structure includes a body, a first fitting hole, a second fitting hole, and at least one elastic engaging member. The first fitting hole is disposed at one end of the body. The second fitting hole is disposed at another end of the body. The at least one elastic engaging member is disposed in the first fitting hole and protrudes toward an inner portion of the first fitting hole along a radial direction of the first fitting hole. When a tool is inserted into the first fitting hole, the at least one elastic engaging member is pressed and deformed by the tool and is thus engaged with the tool. The configuration of the at least one elastic engaging member makes it easier to connect a tool to and remove the tool from the socket structure.