A tire (10) not suitable for running flat 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 sidewall (30) comprises a sidewall insert (90) comprising an elastomeric composition (92) referred to as a rigid elastomeric composition having a modulus at 10% extension greater than or equal to 6 MPa and a maximum thickness (Emax) less than or equal to 5.0 mm.