An apparatus for mounting a tyre (P) on a respective rim (C) of a wheel (R) of a vehicle, comprising: - a frame ; - a chuck , connected to the frame to rotate about an axis of rotation (R1) and connectable to the wheel (R) to entrain it in rotation; - a working tool which is movable relative to the frame towards the wheel (R) to come into contact with the tyre (P); - a bead seating device configured to generate an air flow to be injected between a flange of the rim (C) and a bead of the tyre (P) in order to seat the tyre (P) on the rim (C) of the wheel (R), the bead seating device being movable relative to the chuck along a transverse orientation (T), perpendicular to the axis of rotation (R1), between a rest position (P1), in which the bead seating device is spaced from the rim (C), and a working position (P2), in which the bead seating device is interposed between the flange of the rim (C) and the bead of the tyre (P), the bead seating device including: a rigid element , an injection nozzle connected to the rigid element and configured to be interposed between the flange of the rim (C) and the bead of the tyre (P) when the bead seating device is at the working position (P2); and a duct connected to the injection nozzle to feed the air flow to it, characterized in that , at the working position (P2), the bead seating device is operatively constrained rigidly to the frame and wherein the apparatus comprises a locking device configured to make the rigid element of the bead seating device become one with the frame in its working position (P2), so that the bead seating device remains independently and fixedly stationary at the position (P2), even when subjected to a force generated by the air flow. - a frame ; - a chuck , connected to the frame to rotate about an axis of rotation (R1) and connectable to the wheel (R) to entrain it in rotation; - a working tool which is movable relative to the frame towards the wheel (R) to come into contact with the tyre (P); - a bead seating device configured to generate an air flow to be injected between a flange of the rim (C) and a bead of the tyre (P) in order to seat the tyre (P) on the rim (C) of the wheel (R), the bead seating device being movable relative to the chuck along a transverse orientation (T), perpendicular to the axis of rotation (R1), between a rest position (P1), in which the bead seating device is spaced from the rim (C), and a working position (P2), in which the bead seating device is interposed between the flange of the rim (C) and the bead of the tyre (P), the bead seating device including: a rigid element , an injection nozzle connected to the rigid element and configured to be interposed between the flange of the rim (C) and the bead of the tyre (P) when the bead seating device is at the working position (P2); and a duct connected to the injection nozzle to feed the air flow to it, characterized in that , at the working position (P2), the bead seating device is operatively constrained rigidly to the frame and wherein the apparatus comprises a locking device configured to make the rigid element of the bead seating device become one with the frame in its working position (P2), so that the bead seating device remains independently and fixedly stationary at the position (P2), even when subjected to a force generated by the air flow. <EOS>