A machine for fitting and removing a tyre from a corresponding rim of a wheel for a vehicle, comprising: - a wheel-holder unit rotating about a first vertical axis of rotation; - a column having a guide oriented vertically; - an upper arm and a lower arm, each having a first and a second end; - an upper carriage coupled to the guide of the column and connected to the first end of the upper arm; - an upper operating head, connected to the second end of the upper arm, rotating about a second axis of rotation, provided with at least one upper fitting tool having an elongate shape along a longitudinal direction, to be operatively inserted between a bead of the tyre and an annular edge of the rim and provided with at least one further tool, angularly spaced from the upper fitting tool by a predetermined angle, so that the tools are alternatively selectable by rotating the upper operating head in respective operating configurations in which they are oriented towards the wheel to be positioned in a working position in contact with the tyre by translation of the upper operating head; - a lower operating head, coupled to the second end of a lower arm and provided with at least one tool designed to be operatively acting on a lower bead of the tyre, the second end of the lower arm being slidably coupled to the column, the machine being characterised in that it comprises a wall pressing tool connected to the upper operating head. connected to the upper fitting tool and oriented in a direction concordant with the upper fitting tool for being positioned simultaneously with the upper fitting tool in a working position in which the wall pressing tool and the upper fitting tool are both in contact with the wheel positioned on the wheel-holder unit. - a wheel-holder unit rotating about a first vertical axis of rotation; - a column having a guide oriented vertically; - an upper arm and a lower arm, each having a first and a second end; - an upper carriage coupled to the guide of the column and connected to the first end of the upper arm; - an upper operating head, connected to the second end of the upper arm, rotating about a second axis of rotation, provided with at least one upper fitting tool having an elongate shape along a longitudinal direction, to be operatively inserted between a bead of the tyre and an annular edge of the rim and provided with at least one further tool, angularly spaced from the upper fitting tool by a predetermined angle, so that the tools are alternatively selectable by rotating the upper operating head in respective operating configurations in which they are oriented towards the wheel to be positioned in a working position in contact with the tyre by translation of the upper operating head; - a lower operating head, coupled to the second end of a lower arm and provided with at least one tool designed to be operatively acting on a lower bead of the tyre, the second end of the lower arm being slidably coupled to the column, the machine being characterised in that it comprises a wall pressing tool connected to the upper operating head. connected to the upper fitting tool and oriented in a direction concordant with the upper fitting tool for being positioned simultaneously with the upper fitting tool in a working position in which the wall pressing tool and the upper fitting tool are both in contact with the wheel positioned on the wheel-holder unit.