Carcass plies for radial-ply tires are prepared by coating individual reinforcing strands with a rubber composition, and winding the coated strands in a winding machine with relatively weak transverse circumferential strands into a continuous cylindrical tube in which the reinforcing strands are substantially parallel to the tube axis and circumferentially spaced, and are connected by the circumferential strands of weaker material. Axial sections are cut from the tube, and only the axially central, annular portion of each section is expanded radially during shaping of the carcass, thereby stretching or breaking the transverse, circumferential strands.