The constituent elements of a carcass structure of a tire are formed by laying elementary components on a building support including an inflatable bladder set in an inflated condition in which it substantially reproduces the inner configuration of the carcass structure to be obtained. A belt structure carrying a tread band, both produced separately, is coaxially disposed around the carcass structure formed on the building support and applied thereto following a radial expansion of the inflatable bladder. In a vulcanization mold, the building support is submitted to an over-inflation step to press the tire against the inner walls of the mold. The circumferential edges of the inflatable bladder are in engagement with respective anchoring flanges with possibility of movement in a radial direction, so as to be submitted to an elastic expansion during the over-inflation step.