A tire (10) for a vehicle comprises a radially outermost working layer (41) which comprises at least one undulation (412) in line with a central rib (251) of the tread (2). The undulation (412) is radially on the outside of the points of the working layer (41) in line with the bottom face (243) of the circumferential groove (24) closest to the undulation (412) and has an amplitude of at least 1 mm. The undulation (412) is vertically in line above at least one local reinforcing layer (6) comprising reinforcing elements that are mutually parallel and make with the circumferential direction (XX′) of the tire an angle of which the absolute value is at most equal to 5°.