A carcass ply (3) is built on a forming drum (11) by application of a plurality of strip-like elements (13), through the steps of : setting a width of these strip- like elements (13), setting a width of the overlapped part S between two adjacent strip-like elements (13), setting a fitting diameter of the forming drum (11) by calculating a corresponding extension of a radially external laying surface (14), calculating a whole number (n) of strip-like elements (13) to be applied. The whole number (n) of strip-like elements (13) is applied by rotating the forming drum (11) around a geometric rotation axis (X-X) thereof, and applying pairs of strip-like elements (13) by means of a first laying unit (18) and a second laying unit (19) located close to opposite portions of the forming drum (11) relative to the geometric rotation axis (X-X). When the calculated whole number (n) of strip-like elements (13) is an odd number, before at least one application step, the first laying unit (18) is shifted along an adjustment path (C-C) orthogonal to the geometric rotation axis (X-X) and substantially tangent to the radially external laying surface (14) of the forming drum (11).