There are a lot of technical systems in engineering world that apply tire haulage as signifi cant component of their structure. It is quite obvious that in order to maintain a haulage fl eet in proper conditions the system must possess a preservative subsystem to meet planned maintenance and repair requirements. A suitable organization of this subsystem determines the number of transport units accomplishing the given transportation task. In the paper the problem of proper mathematical description of the system: truck - workshop is being considered employing models taken from the queue theory. The main characteristic that is obtained is the probability distribution of a number of failed trucks as the function of several parameters such as the fl eet size and possession of a reserve, reliability indices of machines and parameters characterizing intensity of realized repairs and number of repair stands.