A tire building drum has a crown section with crown segments which are movable from a crown-down position into a crown-up position, wherein the crown segments together form a crown surface facing outwards in the radial direction, a leading edge and a shoulder that forms the transition from the crown surface to the leading edge, wherein the shoulder leaves a gap, wherein the tire building drum further includes a plurality of support members that extend in said gap, wherein each crown segment has a first side and a second side, wherein each crown segment further includes one or more guide channels, wherein each guide channel is arranged for receiving a respective one of the plurality of support members in the respective crown segment between the first side and the second side. Also disclosed is a method for tire building using the aforementioned tire building drum.