Tire comprising major grooves with a depth at least equal to 4 mm and with a width at least equal to 1 mm. The radially outermost working layer (41) comprises at least one undulation (412). The undulation (412) is such that the undulation (412) portion of the working layer (41) represents at least 10% of the surface of the working layer (41), has an amplitude of at least 1 mm and is radially on the outside of the points of the working layer (41) that are in line with the bottom face (243) of the major groove (24) closest (412). All the layers of material (3, 6, 7) making up the radial stack of the crown structure (S) have mean surfaces parallel to that of the radially outermost working layer (41).