Abstract: The invention relates to the manufacture of seamless tubes by the method of tube rolling. According to the method of the present invention a hollow blank is deformed with regard to its wall thickness, the deformation being alternated at least twice with a reduction of the diameter of the blank by means ofa mandrel with alternating groups of grooves for deformation and groups for reduction. The mandrel diameter at the portions corresponding to the groups of reduction grooves is smaller than the mandrel diameter at the preceding portions corresponding to the groups of grooves designed for deformation of the hollow blank to change the wall thickness thereof. During the continuous rolling, this enables subsequent levelling out of bulges at the tube ends in grooves on the mandrel during the deformation of the blank wall. As a result, the range of rolled tubes is considerably enlarged with an increased production of small-diameter thick-walled tubes and large-diameter thin-walled tubes without bulged ends.