The deformation properties of commercial-purity MChVP molybdenum are studied. Plasticity diagrams that relate the limiting strain to failure to the state-of-stress indices are constructed. The plasticity of the material is found to depend substantially on the type of state of stress, which is characterized by the Lode parameter. The plasticity of the material is analyzed under alternating deformation conditions. A damage theory is used to study the healing of the deformation-induced damage during annealing and to determine the conditions under which irreversible damage, which cannot be healed by heat treatment, appears. The simulation results are used to analyze the damage accumulation during the production of thin-wall pipes. The plasticity margin is found to decrease most strongly during the multipass pressing of a pipe workpiece in a punch. As follows from the damage calculation results, intermediate annealing between pressing passes should be introduced at a size of 18 × 3.1 mm.