A tire building method comprising: feeding an elastomer strip in a feed direction towards a building drum by means of a first and a second feed conveyor arranged in succession; cyclically determining the transverse position of both sides of the elastomer strip in a centring direction perpendicular to the feed direction; calculating an average head out of center on a head portion of the elastomer strip; and moving the second feed conveyor transversely in the centring direction by an amount equal to the average head out of center, before winding the elastomer strip around the building drum.