A machine and method for applying a tread to a carcass of a tire; the machine has a rotary drum supporting the carcass, a feed conveyor for feeding the tread to the rotary drum, a pressure roller contacting the tread, an actuating device for pushing the pressure roller against the tread with a force of adjustable intensity, and a control unit for regulating the intensity of the force as a function of an error variable calculated as the difference between the length of the remaining portion of the circumference of the carcass, and the length of the remaining portion of the tread; and the control unit regulates the intensity of the force by means of a proportional control block having a gain varying as a function of the value of the error variable and as a function of the rate of change of the error variable.