One of the principal failures of the supporting and working rolls on the Quarto rolling system is the spalling of their surfaces due to the gradual accumulation of defects in contact volumes of a material. Nowadays to prevent such kind of degradation failures it is necessary to check out the stationary condition of the contact strength, which doesn’t answer to the question of the duration of the roll staying in the working state, i.e., its resource (lifetime). In the article a new physical-analytical model of the roll’s failure is suggested by the criterion of the surface layer fracture and the corresponding methodology of the expected resource calculation. The approach is based on the kinetic concept of damage of solid bodies, the energy (thermodynamic) condition of fracture of solid bodies and the fundamentals of reliability forecasting for technical objects. The feature of the suggested methodology is that the definition of the failure moment for the supporting or working rolls of the Quarto system derived from the condition of the current density of defects in surface layer of a material reaching the critical value, which is the function of the enthalpy of a material melting.. © 2023 Trans Tech Publications Ltd, Switzerland.