An apparatus for making blanks of a profile varying lengthwise comprising a bed (24), a sizing former (2), a planetary rolling mill (25), a means (26) for feeding the sizing former to said planetary rolling mill (25) wherein said planetary rolling mill (25) comprises work rolls (15), and rims (16) mounted for free rotation in cages of support rolls (14), said planetary rolling mill being fixedly mounted on the bed (24) and having a groove (6) of a constant size, said sizing former (2) being positioned coaxially with the groove (6) and having sizing faces (7) being in the form of concave surfaces (13), the center of each curve (13), taking into account the varying thickness of the profile of a billet (1) being formed, being located on the axis of rotation of a respective support roll (14), said sizing faces (7) being on either side of the groove (6) and being symmetrical with respect to the longitudinal axis of the sizing former (2), each sizing face (7) having a length corresponding to the length of the product between its middle portion and the end thereof, a pair of guide rollers (12) provided between said sizing former (2) and the planetary rolling mill (25) for guiding the billet (1), the guide rollers being positioned symmetrically with respect to the longitudinal axis of said sizing former, a limiting abutment (29) provided on the bed (24) and spaced from the longitudinal axis of the sizing former at a distance equal to one half of the billet length.