Counter-die cylinder (1) for a machine for stamping laminar material, which comprises a cylindrical body (2) that rotates on its own axis, at least one tubular element (3), delimiting two opposite ends, which is arranged on the cylindrical body (2), and at least one shroud (4) arranged around the corresponding said tubular element (3), which further comprises movement means linked to the two opposite ends of the at least one tubular element for moving said tubular element in a longitudinal direction with respect to the axis of the cylindrical body, such that the position of the tubular element can vary along the length of the cylindrical body (2), said movement means being actuated by automated actuation means. In this way, the wear on the shrouds is reduced simply and automatically.