The precision of strip flatness depends on several factors;wear of rolls is one of the main variables that have influence on the surface quality of the strip.The wear of the rolls represents a complex friction condition, sometimes the wear in the backup roll is not analyzed because the strip is not in contact with the backup roll; however,after several campaigns of rolling,the wear in the backup roll becomes dangerous because the pressure distribution is not uniform.Investigation of mechanism of the surface deterioration of the backup roll for the hot strip rolling is very important for the development of the automatic strip shape control system used in hot strip mills.A mathematical model is developed considering the Hertzian pressure distribution between two cylinders with parallel axes.It is used in real time for calculating the wear in the backup roll and in this manner take decisions for preventing finished product reworking or damage of equipments,which result in accidents caused by excessive wear in the backup rolls. The precision of strip flatness depends on several factors; wear of rolls is one of the main variables that have influence on the surface quality of the strip. Wear of the rolls represents a complex friction condition, sometimes the wear in the backup roll is not analyzed because the strip is not in contact with the backup roll; however, after several campaigns of rolling, the wear in the backup roll becomes dangerous because the pressure distribution is not uniform. Investigations of mechanism of the surface deterioration of the backup roll for the hot strip rolling is very important for the development of the automatic strip shape control system used in hot strip mills. A mathematical model is developed considering the Hertzian pressure distribution between two cylinders with parallel axes. It is used in real time for calculating the wear in the backup roll and in this manner take decisions for preventing finished product reworking or damage of equipments, which result in accidents caused by excessive wear in the backup rolls.