A machine for fitting and removing a tyre from a corresponding rim of a wheel of a vehicle, comprising: a wheel-holder unit rotating about a first axis (A) and slidably coupled to a groove provided in a base; a column; an upper operating head, provided with at least one upper fitting tool, at least one further tool, angularly spaced from the upper fitting tool, by a predetermined angle, and a wall pressing tool that can be placed in a working position which is operatively in contact with the wheel simultaneously with the upper fitting tool.