An elastically coupled joint comprises a shaft for transmitting rotary motion, a housing in which the shaft is concentrically inserted, an elastic member provided between the shaft and the housing, and a stopper for preventing excessive displacement between the shaft and the housing. The housing is provided, at an end thereof with a yoke for supporting a spider of a universal joint. The elastic member is provided with a tubular outer ring and a cylindrical elastic body fixed on the inner side of the outer ring. The shaft is pressure fitted into the central portion of the elastic member. The stopper is composed of a pin member inserted in a penetrating hole formed in the housing, the elastic member and the shaft. The penetrating hole may be formed such that the stopper pin is received in the shaft with a press fit, with each end portion of the pin having a predetermined uniform circumferential gap to the housing and the outer ring.