A plurality of strip-like elements is applied onto a forming drum externally having a substantially cylindrical laying surface. The strip-like elements are disposed in mutually approached relationship to form at least one first annular reinforcing layer on the forming drum itself set to a first work diameter at which each of the applied strip-like elements on the laying surface subtends an arc of a circumference of a width as large as a submultiple integer of the overall circumferential extension of the laying surface itself. Adjustment devices operating on the forming drum subsequently carry out expansion of the latter to a second work diameter larger than the first work diameter, while maintaining its laying surface substantially cylindrical.