One of the criteria for assessing the reliability of load-bearing elements of bridges, are peak values of the temporary mobile load significantly exceeding the standard level of loading. Peak loads are interpreted as a continuous random process in the form of a random pulse sequence manifested after a random period of time and having a random duration.Purpose: The aim of the paper is to show changes in temporary mobile load over time in the form of a simple Poissonian flow, where the bridge load is independent, and repeatability and duration of the random load are independent random variables.Research findings: Three cases are considered to determine sufficiently low probability of destructive temporary mobile loads during the given normative service life of bridges. Based on the failure types, the average failure-free operation of the beam is determined as well as the operating time for a possible failure with a prolonged or specific excess load.