The main results of improving in the condition of the surface layer of the working rolls of the training mill with their joint rotation pressed against each other in a state without a trained strip, are considered in order to further minimize changes in the roughness parameters of the trained strip from roll to roll. The analysis of changes in the roughness parameters of the working rolls during their running-in as a result of the elastic-plastic interaction of the microsteps of their surfaces is carried out. Mathematical dependences are obtained for calculating of the roughness parameters of the working rolls during their idle running in the stand, taking into account the ergodicity function of the process. It is shown that the permissible degree of reduction of the height parameters of the rough layer of the working rolls before stabilization during their running is determined by contact loads, physical and mechanical properties of the material of the rolls, the initial parameters of the microgeometry of their surfaces and friction conditions, and the time to stabilize of the roughness parameters depends mainly on the contact load and the speed of running-in, decreasing with decreasing load and increasing speed. It is determined that the maximum possible reduction in the initial roughness of the roll treated with shot after idle running them in a stand with a coefficient of friction of 0.3 is on average 57 %. A further change in roughness is associated with the effect of wear of the rough layer during the training of a cold-rolled strip. The obtained mathematical dependencies allow you to assign processing parameters, such as the compression force of the rolls, the speed or at a given speed — the running-in time.