In the building of a carcass structure for tires of vehicle wheels, the step of reinforcing with a loop at least one annular anchoring structure associated at the axially opposite end edges of a carcass ply is carried out on at least one radially expandable/contractable service drum and includes the steps of: setting the service drum to a predetermined radial dimension selected according to the fitting diameter of the tire to be manufactured, depositing the loop on the service drum, loading the annular anchoring structure onto the service drum in a radially outer position with respect to the loop, radially expanding the service drum up to lock in position the annular anchoring structure, rotating the service drum about a longitudinal axis thereof and, during the rotation, turning the loop up about the annular anchoring structure.