Abstract: A machine intended for back muscular training includes a seat (2) carried by a stand, a back rest (17) situated above the seat, as well as a main arm (12) which is turnable around a main joint (13) against the effect of a loading device (3). The back rest (17) is spaced from the seat and connected to a part of the main arm (12) extending upwards from the main joint (13), more precisely via a rocker arm (19) turnable around a secondary joint (20) on the main arm, which rocker arm has a cross boom (18), extending at an angle to the same on which the back rest is mounted. In this way, the back rest (17) is movable between a front starting position and a rear end position in an orbital path along which the back rest—thanks to the mounting thereof on the rocker arm (19)—can move freely between different radial positions in relation to the main joint (13) depending on the individual back flexing movements of individual users.