A tire building drum has a drum shaft and a circumferential surface for receiving a tire component, wherein the circumferential surface is defined by segments which are radially movable between a contracted position in which the circumferential surface has a first radius and an expanded position in which the circumferential surface has a second, greater radius. The tire building drum includes cover plates, wherein each segment is provided with a first section having a first support surface for supporting the tire component and a second section with a second support surface for supporting the cover plate. Each second section is movable relative to its respective first section from a recessed position in which the second support surface is recessed with respect to first radius and an extended position in which the second support surface is raised towards the second radius.