Building a carcass structure in the manufacturing of a tire for vehicle wheels includes associating, at each end edge of a carcass ply laying on a forming support, at least one respective annular reinforcing structure obtained by depositing at least one respective reinforcing element. The deposition of the at least one respective reinforcing element includes feeding a continuous reinforced band-like element at a cutting unit, cutting to size at least one first reinforcing element from the continuous reinforced band-like element, moving the first reinforcing element from the cutting unit toward a first end edge of the carcass ply, positioning the first reinforcing element on the first end edge, cutting to size at least one second reinforcing element from the continuous reinforced band-like element, moving the second reinforcing element from the cutting unit toward a second end edge of the carcass ply opposite said first end edge, and positioning the second reinforcing element on the other end edge.