The invention relates to an aircraft tire (1) including: two beads (2), each intended to come into contact with a rim (3) via at least one radially inner bead surface (4); and a carcass reinforcement (5) including at least one carcass layer (6) that connects the two beads (2), each carcass layer (6) being wound inside each bead (2) around a bead wire (7) having a central meridian section (O). In each bead (2), a portion (8) for clamping under the bead wire extends radially inside a portion (5) of the carcass reinforcement, located radially inside the bead wire (7), as far as the radially inner bead surface (4). The portion (8) for clamping under the bead wire includes a surface layer (9) intended to come into contact with the rim (3) via the radially inner bead surface (4), said layer having a shear stiffness K1. The inventors aim to reduce the speed at which critical defects or "pits" form on the rim seat, so as to extend the life of the rim and thus increase the number of use cycles prior to its removal from service. According to the invention, the portion (8) for clamping under the bead wire includes: a rigid layer (10) located radially outside and adjacent to the surface layer (9) and having a shear stiffness K2 at least equal to five times the shear stiffness K1 of the surface layer (9); and a deformable layer (11) that is located radially outside and adjacent to the rigid layer (10) and radially inside and adjacent to the carcass reinforcement portion (5) which is radially inside the bead wire (7), said deformable layer having a shear stiffness K3 at most equal to 0.3 times the shear stiffness K1 of the surface layer (9).