The article proposes an analytical method for designing optimal modes of finishing of backup rolls of hot sheet rolling mills in order to ensure their maximum feasible service life. It is based on the known models of backup roll failure according to the kinetic strength and material wear resistance criteria and, therefore, it includes the following stages. The calculation of value ranges of the roll design life according to the wear profile distortion and contact fatigue criteria for the interval of the roughness Ra parameter change determined in the technological instruction. The selection of the maximum service life value and its corresponding parameter Ra that provide the operational integrity of the rolls simultaneously based on these two criteria. The calculation of the optimal grinding modes for the formation of the estimated value of the standard profile deviation Ra with one of the known empirical dependence.The example of designing the industrial tested optimal modes of roll grinding has proved operational effectiveness of the method. It was determined that roll grinding based on the calculated modes leads to a 10-12 percent increase in their service life.