A method of manufacturing a carcass structure for vehicle tires includes preparing strip sections, each comprising longitudinal and parallel thread elements coated at least partly with at least one layer of raw elastomer material. A first series of strip sections is laid down onto a toroidal support. First primary portions of annular reinforcing structures are applied against end flaps of the first series strip sections. At least one second series of strip sections is laid down onto the toroidal support. Together, the first and second series define a first carcass ply. A third series of strip sections is laid down onto the toroidal support. Second primary portions of the annular reinforcing structures are applied against end flaps of the third series strip sections. At least one fourth series of strip sections is laid down onto the toroidal support. Together, the third and fourth series define a second carcass ply.