Abstract: Machine for fitting and removing a tire (1) from a rim (2) of a wheel (3). The machine comprises a frame (10), a rotating table (11) in order to attach the wheel thereto by its rim and to rotate the rim about its axis (Y), and a tool (12) for fitting and/or removing the tire from the rim. The tool (12) is connected to the frame (10) by means of a movable structure (20) capable of moving the tool (12) horizontally and vertically to its working position situated close to the proximal edge (4) of the rim (2) when the wheel (3) is mounted on the rotating table (11). The movable structure (20) comprises four arms (A, B, C, D) connected together in twos by means of four pivots (p, q, r, s) the axes (X1, X2, X3, X4) of which are parallel with one another. One of the arms (A) is secured to the frame (10) and the tool (12) is connected to one of the other arms (B, C, D).