A machine for mounting and demounting a tyre relative to a corresponding rim of a vehicle wheel, comprising: - a frame provided with a column extending along a vertical direction; - a wheel-holder unit, movable in rotation about a vertical axis of rotation and in translation towards and away from the column along a horizontal axis of translation; - a supporting arm, connected to the column; - a mounting tool, connected to the supporting arm and configured to operatively engage the tyre in order to mount the tyre to the rim; - a demounting tool, configured to operatively engage the tyre in order to demount the tyre from the rim; - a main arm, extending above the wheel-holder unit between a first end that is operatively connected to the column, and a second end; - a working unit, connected to the main arm and including: a first arm pivoted at a hinge point to the second end of the main arm to rotate about the hinge point, where the hinge point lies in a plane that includes the vertical axis of rotation and the horizontal axis of translation, and a first sidewall pressing tool, connected to the first arm and configured to come into abutment against a sidewall of the tyre of the wheel mounted on the wheel-holder unit, the working unit is movable along the vertical direction between a working configuration, where it is close to the wheel-holder unit and a rest configuration, where it is raised and distal from the wheel-holder unit, the machine being characterized in that the main arm is movable by translation along a movement axis parallel to, and spaced from, the horizontal axis of translation towards and away from the column to keep the hinge point vertically aligned with the vertical axis of rotation of the wheel-holder unit, responsive to a movement in translation of the wheel-holder unit. - a frame provided with a column extending along a vertical direction; - a wheel-holder unit, movable in rotation about a vertical axis of rotation and in translation towards and away from the column along a horizontal axis of translation; - a supporting arm, connected to the column; - a mounting tool, connected to the supporting arm and configured to operatively engage the tyre in order to mount the tyre to the rim; - a demounting tool, configured to operatively engage the tyre in order to demount the tyre from the rim; - a main arm, extending above the wheel-holder unit between a first end that is operatively connected to the column, and a second end; - a working unit, connected to the main arm and including: a first arm pivoted at a hinge point to the second end of the main arm to rotate about the hinge point, where the hinge point lies in a plane that includes the vertical axis of rotation and the horizontal axis of translation, and a first sidewall pressing tool, connected to the first arm and configured to come into abutment against a sidewall of the tyre of the wheel mounted on the wheel-holder unit, the working unit is movable along the vertical direction between a working configuration, where it is close to the wheel-holder unit and a rest configuration, where it is raised and distal from the wheel-holder unit, the machine being characterized in that the main arm is movable by translation along a movement axis parallel to, and spaced from, the horizontal axis of translation towards and away from the column to keep the hinge point vertically aligned with the vertical axis of rotation of the wheel-holder unit, responsive to a movement in translation of the wheel-holder unit. a first arm pivoted at a hinge point to the second end of the main arm to rotate about the hinge point, where the hinge point lies in a plane that includes the vertical axis of rotation and the horizontal axis of translation, and a first sidewall pressing tool, connected to the first arm and configured to come into abutment against a sidewall of the tyre of the wheel mounted on the wheel-holder unit, the working unit is movable along the vertical direction between a working configuration, where it is close to the wheel-holder unit and a rest configuration, where it is raised and distal from the wheel-holder unit,