Oil spill caused by the erosion in elbows is widely encountered in long-distance crude oil transmission pipelines and will lead to a considerable economic loss and potential safety hazards. In order to prevent the equipment failure and evaluate the campaign life of piping systems, there exists an urgent need to identify the positions suffering severe erosion damage and predict the erosion rate in pipelines for multiphase flow. In this study, a mathematical model is established to predict the solid particle erosion in the elbows of petroleum pipelines, in which the particle-fluid interaction is taken into account. The effects of bend orientation and particle properties on the erosion process are investigated in details. In order to understand the erosion mechanism related with the dynamic behavior of flow fluid and entrained particles, the relationship between the secondary flows and the particle trajectories is analyzed emphatically. The results indicate that erosion mainly occurs in the regions near the elbow exit, especially the side walls of the downstream straight pipe and extrados of the bend section. However, erosion on the side walls could not always happen when the effect of the secondary flows is not remarkable. It is also found that the erosion behavior depends upon both the centrifugal effect of pipe flow and the forces acting on particles. Finally, an erosion pattern based on Stokes number is developed to quantify the complex coupled effects of the flow field and particle properties. (C) 2016 Elsevier B.V. All rights reserved.