A working head for an apparatus for mounting and demounting a tyre to and from a corresponding rim of a vehicle wheel, the working head comprising: - a contoured element, having a first end and a second end, spaced from each other along a longitudinal orientation, wherein the first end faces in a first direction and defines a connecting zone of the contoured element and the second end faces in a second direction, opposite to the first direction and defines a supporting zone of the contoured element, adapted to abut against the wheel rim with the contoured element in sliding contact with the rim, the contoured element including a demounting guide, adapted to come into sliding contact to guide the wheel tyre, and a mounting guide, juxtaposed with the demounting guide along a transverse orientation perpendicular to the longitudinal orientation and adapted to come into sliding contact to guide the tyre while it is being mounted to the wheel rim; - a gripping tool, movable in a working plane perpendicular to the transverse orientation and parallel to the longitudinal direction between a gripping position, where it is operatively interposed between the rim and the tyre, and a prising position, where the gripping tool is lifted longitudinally relative to the second end of the contoured element; a transmission unit connectable to an actuator and to the gripping tool and configured to move the gripping tool between the gripping position and the prising position responsive to a movement of the actuator, wherein the demounting guide is interposed, along the transverse orientation, between the gripping tool and the mounting guide of the contoured element, and wherein the contoured element is removably connected to an arm of the apparatus, characterized in that the contoured element is made as a single part, made of polymeric material. - a contoured element, having a first end and a second end, spaced from each other along a longitudinal orientation, wherein the first end faces in a first direction and defines a connecting zone of the contoured element and the second end faces in a second direction, opposite to the first direction and defines a supporting zone of the contoured element, adapted to abut against the wheel rim with the contoured element in sliding contact with the rim, the contoured element including a demounting guide, adapted to come into sliding contact to guide the wheel tyre, and a mounting guide, juxtaposed with the demounting guide along a transverse orientation perpendicular to the longitudinal orientation and adapted to come into sliding contact to guide the tyre while it is being mounted to the wheel rim; - a gripping tool, movable in a working plane perpendicular to the transverse orientation and parallel to the longitudinal direction between a gripping position, where it is operatively interposed between the rim and the tyre, and a prising position, where the gripping tool is lifted longitudinally relative to the second end of the contoured element; a transmission unit connectable to an actuator and to the gripping tool and configured to move the gripping tool between the gripping position and the prising position responsive to a movement of the actuator, wherein the demounting guide is interposed, along the transverse orientation, between the gripping tool and the mounting guide of the contoured element, and wherein the contoured element is removably connected to an arm of the apparatus, characterized in that the contoured element is made as a single part, made of polymeric material.