For researchers in the fields of cartography and graph drawing, the placement problem of text labels for the corresponding graphical objects is a challenging issue they may often encounter. This work focuses on studying the problem of placing rectangular text labels onto a set of fixed disks possibly with overlapping such that users may easily recognize the disks and labels, and the correspondence relationship between the disks and the corresponding labels by just visualising the layout of the disks and the labels. In this paper, we propose an innovative method based on force-directed mechanism to place labels at the appropriate locations with respect to the given positions of the disks. The method starts by placing the given labels at the centers of their corresponding disks respectively, and proceeds with pushing around the labels via applying specific attractive and repulsive forces between the disks and labels so that the overlapping situation between the labels are greatly improved or even completely eliminated, and the correspondence relationship between the disks and the corresponding labels become more easily recognizable. User survey results show that our method is effective in producing outputs with both good visibility rates of disks and labels and good correspondence rate between disks and the corresponding labels. The applications of such a label placement problem studied include labeling a set of circular regions appeared in the real world, such as labeling a set of signal coverage zones of the base stations in the cellular telephone network of some telecommunication company in an urban city.