Maintaining high efficiency of using the fleet of public mass transport vehicles puts many challenges ahead of the operator. Among them, when planning periodic operational activities, the operator should take into account the assessment of possible unexpected vehicle failures and the costs of their removal under the so-called corrective maintenance. Due to the random nature of vehicle breakdowns, knowledge about stochastic processes is necessary to maintain their efficient and safe operation. The research problem formulated in the title meets these needs. Therefore, the costs of corrective maintenance of vehicles are modelled, i.e. the costs that are not included in the scheduled maintenance costs and are not related to preventive maintenance. The costs of corrective maintenance and the costs of replacement of damaged parts are unexpectedly created at random moments of operating means of transport, usually between scheduled maintenance. Due to the variety of failure processes of individual parts of the vehicle, the methods and applications of stochastic modelling for simple failures modelled by the Poisson process are presented in this paper. The basis for the application of the presented methods is to identify those parts of the vehicle that are damaged in accordance with this process. The assessment of parameters of failure processes of individual vehicle parts is made on the basis of the operational database of a homogeneous fleet of vehicles operated for 5 years. The operational database is dynamically updated with new events. On the basis of actual data on corrective maintenance of a distinguished group of damaged parts of vehicles, the possibilities and limitations of practical applications of the Poisson process to assess the risk of incurring costs in the further process of fleet operation were shown.