A tire for a vehicle wheel, comprising two sidewalls joined by a crown zone provided on its radially outer portion with a circumferential tread, a bead arranged at the radially inner portion of each of the sidewalls, each bead comprising a seat and an outer flange which are intended to come into contact with the rim. The bead seat has a generatrix, the axially inner end of which lies on a circle of diameter greater than the diameter of the circle on which the axially outer end is located. A carcass-type reinforcement structure extends substantially radially from each of the beads, along the sidewalls, towards the crown zone, such bead being reinforced by a substantially radial arrangement of circumferential cords arranged in stacks. A portion of the carcass-type reinforcement structure is arranged in the immediate vicinity of at least one portion of a stack, and the space between these portions is generally occupied by a rubber mix of high elasticity modulus.