Abstract The main aim of the present paper is the distribution of relative deformation in rolling zone; due to the fact that relative deformation along the length of contact arc is changed. Mathematical analysis of the distribution of relative deformation covers elliptic distribution. Average value of relative deformation in rolling zone was obtained as integral value which more accurately describes total quantity of deformation. The present result shows that average value of relative deformation in rolling zone is not equal to total deformation for one pass, that means is possible to take into consideration for invariable equal to 2/3. Invariable of rolling zone equal to 2/3 is usable to evaluate resistance deformation from strain hardening curve by cold rolling. Calculated resistance deformation through rolling invariable more accurately describes actual value of resistance deformation.