У роботі визначаються показники надійності та ресурс напівпричепу автоцистерни на основі імовірнісних характеристик вібрацій елементів конструкції підчас її руху по дорогам з покриттям різної якості. Досліджується випадковий вплив навантаження з урахуванням його запізнення у часі на задній вісі транспортного засобу. За допомогою метода скінченних елементів та методів статистичної динаміки визначені ймовірнісні характеристики поведінки системи. Запропоновано підхід до оцінки надійності конструкції за критерієм накопичення втоми. The paper presents the determination of reliability and life-time of semi-trailers based on random vibrations of driving on roads with different qualities. Damage to the tank capable appears during operation due to the accumulation and development of fatigue or corrosion, which leads to cracks and depressurization boiler tank. Therefore, development of methods for modeling settlement tank designs to assess their durability and reliability prediction at the design stage and in operation to ensure safety is important for practical problem. For solving problem random vibrations of vehicle with the influence of the lag effect the mathematical model was made. Particularly was considered the mathematical model random impacts vector with lag time effect on axis of vehicle. Finite-element model of the boiler semitrailer tanker was developed. The next step was obtained probabilistic behaviors of the system, such as spectral density and standard deviation of stresses, the influence of the lag effect of external forces using the methods of statistical dynamics. When analyzing the standard deviation at stresses determined that there are dangerous zone near the supports and hatches. Using probabilistic characteristics were obtained determine the parameters of reliability. For each type of load has been calculated effective frequency. The main influence on it was the speed of vehicle, but not the quality of the road surface. The approach to assessing the reliability of construction was offered by criteria for the accumulation of fatigue. The graph probability of failure-free operation is life-time has been defined for all types of loading. In the investigation of the life-time was determined that the quality declines of the road at a speed of 90 km / h life-time decreases rapidly.