The invention relates to an elastic coupling device of a circuiting pump. The elastic coupling device is a coupling for connecting the shaft end of a motor with the shaft end of the circulating pump and is used for solving the problem that time and energy are wasted when an elastomer is replaced. The coupling is formed by occluding two half couplings with symmetric structures, and the elastomer is placed on a position where the two half couplings are occluded; each of the half couplings comprises a coupling body and a coupling detaching body; the coupling body is composed of a body pipe part with a half shaft hole and a body head with a shaft hole, the body pipe part is provided with a plurality of bolt through holes, the height of the body head is larger than the double heights of the body pipe part, the body pipe part and the lower half part of the body head are connected into a whole, and the body head is provided with a coupling occluding structure; and the coupling detaching body and the body pipe part are symmetric in structure, the coupling detaching body is provided with bolt through holes as much as the bolt through holes of the body pipe part, the coupling detaching body is arranged on the upper half part of the body head, and bolts and the body pipe part are detachably connected to form a pipe part surrounding and fastening the shaft end of the motor or the shaft end of the circulating pump. By using the coupling, the operation of replacing the elastomer can be performed safely, conveniently and rapidly.