The paper deals with exploration of the probabilistic characteristics of the deformed state and stress concentration of a pipeline section with corrosion damage considering its random spatial shape. The investigation was done based on 3D FE models. A special algorithm is developed for the direct solid modeling of the corroded area in the upper surface of the pipe. A series of 3D models of a pipe with a volumetric surface defect, which has a random shape, is created based on the developed algorithm. An analysis of a probable stress concentration values for different statistical parameters of corrosion defect was carried out in the frame work of Monte-Carlo simulations. The statistical analysis of the system response allowed us to obtain the conditional probability density functions of the maximum stress concentration variation. It was done taking into account the level of the maximum corrosion depth. This information together with statistical data on the corrosion rate obtained from the references gave us a possibility to propose a method to estimate a reliability of a corroded pipe in operation.