Method and apparatus for assembling a tire carcass comprising a precarcass band and a pair of inextensible bead rings. The band is built and consolidated on a form having a rigid cylindrical surface. The band includes at least one cord or wire-reinforced ply and one or more tire liners of a rubbery gum, and may include additional tire components, in particular the components which will form the sidewalls of the tire. The band is removed from its building form and then moved axially freely over a shaping apparatus. An axially narrow central part of the band is expanded sufficiently to resist axial displacement of the band, which is then spread and smoothed outward from its central part by expanding and then moving outwardly a pair of expandable spreading elements. Following the spreading operation, end regions of the band are expanded to seat the prepositioned inextensible bead rings, after which the bead rings are moved axially toward each other and the band therebetween is expanded by air pressure into engagement with a circumferentially restricting ring or belt. With the carcass so expanded, the band endings are turned outwardly about the bead rings by turnup bladders while a pair of annular inner support bladders exert circumferentially uniform axially outward counter-force to squeeze the respective beads.