The object of this study is the process of functioning of the hydrogen storage and supply system. The issue of fire-explosive events in the hydrogen storage and supply system is investigated. A set of mathematical models has been built to determine the probability of a combustible medium in the hydrogen storage and supply system. This set includes partial mathematical models for the main elements of the system, which are united by a generalized mathematical model. When constructing partial mathematical models, the probabilities of trouble-free operation of the main elements of the system are used, which include a pipeline and a gas generator with a pressure stabilization circuit. The probability of trouble-free operation is represented in the form of two multiplicative components that take into account catastrophic and parametric failures of the main elements of the system. When determining the probability of trouble-free operation of the main elements of the system in relation to parametric failures, the integral (generalized) parameters were used. In particular, for a gas generator, such parameters are its time constants. The current values of time constants of the gas generator are determined according to the developed algorithm whose feature is the use for its implementation of the values of the amplitude-frequency characteristics of the system, which are determined at three a priori given frequencies. For a typical version of the on-board hydrogen storage and supply system, quantitative indicators of the likelihood of a combustible medium are given. It is shown that if the parametric failures of the main elements of the system are not taken into account, an error occurs, the value of which is 30.0 %. The results could be used to obtain an express assessment of the level of fire hazard of hydrogen storage and supply systems at different stages of their life cycle.