During building of a carcass structure, a liner is applied around an outer surface of a primary drum by: circumferentially winding at least one pair of sheets of elastomeric material around an outer surface of the primary drum, which sheets are axially spaced apart from each other so as to form respective axially external portions of the liner; laying at least one continuous elongated element of elastomeric material in the form of a plurality of mutually approached coils around the outer surface of the primary drum in order to form a central portion of the liner having axially external edges that are each associated with an axially internal edge of one of said axially external portions of the liner.