The press (1) for curing a green tyre has: a frame (2), at least one plate (4) that is mounted in a sliding manner with respect to the frame and comprises a plurality of pegs (22), a plurality of sectors (8) that are distributed circumferentially around the plate and are able to form all or part of the width of a tread of the tire, and, for each sector, at least one rocker (15) having at least one ramp (19) over which one of the respective pegs is able to pass.