A study of the stress-strain state of metal by the finite element method has been carried out to determine the limiting modes of periodical drawing without exhausting the plasticity resource. It was found that during a mandrel moving cycle, a particle passes three stages of alternating strain the stressed state of which is different. An algorithm and a program for PC calculation of damage of metal being deformed along the motion path of a particle were developed. The damages accumulated in the processes of periodical drawing, cold roller rolling and long mandrel drawing of tubes are compared. It is shown that damage during periodical drawing is much less due to more pronounced alternating deformation. The results of the studies allows us to recommend the above method for production of cold-deformed tubes of ductile alloys (of L96 type) with a reduction ratio less than 8 and those of less ductile alloys with a reduction ration of about 4/6.