An elastic snapping device includes an elastic cord having two distal ends each formed with an end opening, a snapping tool mounted on the elastic cord and having a distal end formed with an enlarged plug inserted into the end opening of the elastic cord, and an elastic sleeve mounted on a connection of the elastic cord and the snapping tool. Thus, the elastic sleeve is mounted on the connection of the elastic cord and the snapping tool closely, so that the snapping tool is combined with the elastic cord rigidly and stably, thereby preventing the snapping tool from detaching from the elastic cord during a long-term utilization.