A tire (10) comprises a crown block (12), two beads (32), and two sidewalls (30) connecting each bead (32) to the crown block (12). The crown block (12) comprises a crown reinforcement (16) comprising a corrugated crown layer (24, 26, 28) comprising corrugations. The tire (10) comprises a sidewall insert (90) comprising a rigid elastomeric composition (92, 93, 94) of which the radially exterior end (96) is arranged: radially to the outside of the equator (E) of the tyre, and axially to the inside of the axial end (241, 242) of the radially innermost crown layer (24) of the crown reinforcement (16) and at an axial distance ENG20 mm from the axial end (242).

A tire (10) comprises a crown block (12), two beads (32), and two sidewalls (30) connecting each bead (32) to the crown block (12). The crown block (12) comprises a crown reinforcement (16) comprising a corrugated crown layer (24, 26, 28) comprising corrugations. The tire (10) comprises a sidewall insert (90) comprising a rigid elastomeric composition (92, 93, 94) of which the radially exterior end (96) is arranged: radially to the outside of the equator (E) of the tyre, and axially to the inside of the axial end (241, 242) of the radially innermost crown layer (24) of the crown reinforcement (16) and at an axial distance ENG20 mm from the axial end (242).