The paper addresses the problem of material fracture in cross rolling processes. A new test based on rotary compression for determining limit values of the damage function after the Cockroft-Latham criterion is proposed. A FEM analysis is performed to determine the stress and strain states in a workpiece subjected to this test. The numerical results demonstrate that the axial region of the workpiece is characterized by the presence of alternating tensile and compressive stresses conducive to fracture. The distribution of the Cockroft-Latham integral in the axial region of the workpiece is determined.