Soundproof tyre (100) along with a process for the production thereof, wherein the tyre comprising particular polyolefin sound absorbent foams that show damping performances for the noise generated in the cavity of such tyre, together with resistance to hydrolysis, poor water absorption and an unexpected thermal and mechanical stability in use conditions, wherein the sound absorbent material (301) is applied at least on one portion of the radially inner surface (113) of the tyre, preferably of the impermeable elastomeric material layer (112), wherein said sound absorbent material comprises a foamed polyolefin material with closed macrocells characterised by an average size of at least 1.5 mm, more preferably of at least 3 mm, still more preferably of at least 4 mm according to ASTM D3576.