In the field of tire building, underbelt inserts are applied to an expandable support associated with an auxiliary drum on which the belt structure is made, simultaneously with manufacture of a carcass structure on a primary drum. Following expansion of the expandable support, the underbelt inserts are applied to the belt structure that can be directly made on the support itself in an expanded condition. The belt structure together with the underbelt inserts and a tread band are then transferred onto the carcass structure formed on the primary drum to complete building of the tire following shaping of the carcass into a toroidal conformation.