The present invention relates to an elastic coupling (1) between rail vehicle wagons, comprising: an end support (2) or curved head (8) in turn comprising a screwed straight area (5), an intermediate deformation area (6) and an end coupling area (7), the end (8) of the coupling area (7) being curved, an end support (3) or straight head (8′) in turn comprising a screwed straight area (5′), an intermediate deformation area (6′) and an end coupling area (7′), the end (8′) of the coupling area (7′) being straight, and an enclosing case (4) covering the end coupling area (7) of the support (2) and the end coupling area (7′) of the support (3), such that the supports (2) and (3) are attached to one another by draw connection means and by elastic elements. The walls of the intermediate area 6 of the support 2 are curved inwards, and the walls of the intermediate area 6′ of the support 3 are curved outwards.