This article presents the results of an experimental study of cold rolling TRB strips of S235JR steel applying one grooved roll and another plain roll. The purpose of the study was to determine the possibility of rolling TRB strips with the technology studied, depending on the dimensions of the charge and the number of rolling passes. In addition, the possibility of reducing the magnitude of TRB strip curvature due to the introduction of asymmetry into the process was investigated. The effect of the rolling process and shape variation on the material’s hardening was evaluated by measuring hardness. Based on the results, it was determined that the greater the initial thickness of the charge, the higher the shape tolerances can be obtained. In addition, hardness variation was observed on the cross-section of TRB strips, which decreased with increasing values of plastic deformation. It has also been shown that it is possible to reduce the curvature of the TRB strip due to the use of double asymmetry.