Abstract The aim of this work was to evaluate the value of equivalent strain and also the temperature effect in tested material after rolling process with additional, cyclic, axial motion of the rolls. This type of rolling is called MEFASS (Metal Forming Aided by Shear Stresses). Research were conducted in Department of Process Modelling and Medical Engineering of Silesian University of Technology, where laboratory rolling mill with possibility of cyclic, axial rolls motion was designed and built. The mathematical relation for calculating the equivalent strain value in MEFASS rolling process is presented. It is observed that change of the strain path in MEFASS rolling causes significant increase of equivalent strain value. It is also observed that part of total equivalent strain connected with rolls axial motion is considerable larger than total equivalent strain connected with change of strip height. The equivalent strain influence in MEFASS rolling on temperature of rolled strip was also discussed in this paper. Temperature of rolled strip was measured by thermovision camera IR Snapshot 525. Thermovision pictures of samples after second pass of non-conventional rolling were the subject of analysis. Increase of strip temperature after MEFASS rolling was observed in comparison with conventional rolling. The value of temperature depends from parameters of MEFASS rolling process: draft quantity, rolling velocity, amplitude and frequency of additional, cyclic, axial rolls motion.