Abstract. At present, due to the complexity of technical systems, industrial production is becoming a source of accidents, disasters, leading to large human and material losses, as well as to environmental pollution. In particular, this applies to conveyor systems for mining enterprises. The main causes of accidents and disasters in the conveyor transport of mining enterprises are the influence of the external environment, the reliability of equipment, as well as the level of operation. The experience of conveyor transport operating at mining enterprises has shown that a large number of accidents on conveyor belts is associated with failures of the frame. This is due to the fact that when the belt with a load moves along the conveyor frame, dynamic loads arise on the roller bearings leading to the failure of the pillow-blocks. At the same time, as the analysis of the data on operation of the belt conveyors shows, accidents that occur because of the rollers failure often lead to large material losses. These material losses are associated with the destruction of the rollers of the roller supports, as well as with the rupture of the conveyor belt. In addition, the elimination of accidents at the line of belt conveyors often lead to long downtime of the entire conveyor transport and, as a result, to a loss of its productivity. In this paper, on the basis of the theory of random Markov processes of death and reproduction, the risk rate in case of failure of the belt conveyor frame is determined by the factor of the rollers failure of the roller supports. The risk rate was determined as a mathematical expectation of the product of the probability of failures of rollers by the value of material losses caused by downtime of the conveyor and repair of roller supports. As a result, the dependence of the risk rate of failure of the belt conveyor frame on the conveyor productivity, the intensity of failures and recovery of the rollers of the roller supports, as well as on the average resource of the rollers, was obtained. It is established that with an increase in the conveyor productivity, the risk of failure of the belt conveyor becomes linear, and with a decrease in the recovery rate of the roller support, the risk increases according to the hyperbolic law. At the same time, with an increase in the failure rate of rollers, the rate of risk increases. In addition, with an increase in the resource of the rollers of the belt conveyor rollers bearings, the rate of the risk of failures of the frame decreases. It is established that the maximum rate of risk has the frame of a belt conveyor with rigid roller supports, and the minimum – the frame of a belt conveyor with shock-absorbed roller supports. Keywords: belt conveyors, frame, roller supports, risk rate.