A flat cylindrical carcass band is built on a cylindrical surface provided by a unique shaping means and abutting turnup means. The shaping means has inner and outer walls the ends of which are juxtaposed solid elastomeric end rings so as to form an annular envelope. The outer wall has between its inner and outer layers an arrangement of spring blades of particular shape formed to control the toroidal shape of the expanded outer wall to a precisely determined contour. The turnup means each include an inner and an outer bladder the edges of each being also juxtaposed solid elastomeric end rings. The end rings of each turnup means are seated with the associated end rings of the shaping means in a common retaining groove formed in a circumferential set of radially extendable segments which expand the end rings and the overlying carcass to conform the carcass initially about prelocated bead cores. To conform the carcass about the bead cores before fully shaping the carcass toroidally, the shaping means has also a pair of inner bladders each having a solid elastomeric ring interfitting respectively with and between the end rings of the mentioned envelope. These latter inner bladders cooperate on inflation to roll the carcass band lying close to the respective beads outwardly and to compact the bead region, and thereafter the shaping means envelope is inflated to shape the carcass between the bead regions and the outer bladder of the turnup means is inflated to extend the turnup, and optionally, to apply sidewall material.