A self-supporting tire for vehicle wheels comprising • a carcass structure comprising at least one carcass ply having opposing side edges associated with respective bead structures; • a belt structure applied in a radially external position with respect to said carcass structure; • a tread band applied in a radially external position with respect to said belt structure; • a pair of sidewalls respectively applied in an axially external position on the side surfaces of said carcass structure; • a layer of air-impermeable elastomeric material, known as a liner, extending at least in correspondence with said tread band in a radially internal position with respect to said carcass structure; and • a pair of sidewall reinforcement inserts, respectively embedded in correspondence with said pair of sidewalls in an axially internal position with respect to said pair of sidewalls, characterised in that • said carcass ply comprises a plurality of hybrid reinforcing cords, each cords having at least two strands corded to each other with a predetermined twisting pitch, wherein each of said at least two strands comprises: ∘ at least one monofilament textile thread; ∘ at least one multifilament textile yarn comprising a plurality of textile filaments; wherein, in any cross-section of the hybrid reinforcing cord, said at least one monofilament textile thread is at least partially embedded in the filaments of said at least one multifilament textile yarn, and • at least one sidewall reinforcement insert of said pair of sidewall reinforcement inserts comprises a vulcanised elastomeric compound having a value of elastic dynamic shear modulus G' equal to or lower than 1.25 MPa measured at 70°C, 10 Hz, 9% strain according to the RPA method set forth in the present description. • a carcass structure comprising at least one carcass ply having opposing side edges associated with respective bead structures; • a belt structure applied in a radially external position with respect to said carcass structure; • a tread band applied in a radially external position with respect to said belt structure; • a pair of sidewalls respectively applied in an axially external position on the side surfaces of said carcass structure; • a layer of air-impermeable elastomeric material, known as a liner, extending at least in correspondence with said tread band in a radially internal position with respect to said carcass structure; and • a pair of sidewall reinforcement inserts, respectively embedded in correspondence with said pair of sidewalls in an axially internal position with respect to said pair of sidewalls, characterised in that • said carcass ply comprises a plurality of hybrid reinforcing cords, each cords having at least two strands corded to each other with a predetermined twisting pitch, wherein each of said at least two strands comprises: ∘ at least one monofilament textile thread; ∘ at least one multifilament textile yarn comprising a plurality of textile filaments; wherein, in any cross-section of the hybrid reinforcing cord, said at least one monofilament textile thread is at least partially embedded in the filaments of said at least one multifilament textile yarn, and ∘ at least one monofilament textile thread; ∘ at least one multifilament textile yarn comprising a plurality of textile filaments; • at least one sidewall reinforcement insert of said pair of sidewall reinforcement inserts comprises a vulcanised elastomeric compound having a value of elastic dynamic shear modulus G' equal to or lower than 1.25 MPa measured at 70°C, 10 Hz, 9% strain according to the RPA method set forth in the present description.