A carcass ply is built on a forming drum by application of a plurality of strip-like elements, through the steps of: setting a width of these strip-like elements, setting a width of the overlapped part between two adjacent strip-like elements, setting a fitting diameter of the forming drum, calculating a whole number of strip-like elements to be applied. The whole number of strip-like elements is applied by rotating the forming drum around a geometric rotation axis thereof, and applying pairs of strip-like elements by means of a first and second laying unit located close to opposite portions of the forming drum. When the calculated whole number of strip-like elements is an odd number, the first laying unit is shifted along an adjustment path orthogonal to the geometric rotation axis and substantially tangent to the radially external laying surface of the forming drum.