Reinforced concrete structures are generally designed to allow cracking under service loading. Accurate modeling of crack formation and propagation at lower load levels is therefore important. In this paper, a Material Failure Process Analysis code (MFPA2D) is used to model the crack initiation and propagation in reinforced concrete bridge pier subjected to eccentric loading. In our numerical model, the reinforced concrete is assumed to be a three-phase composite composed of concrete, reinforcement and interfaces between them. Numerically obtained results of cracking loads and global load-displacement response agree well with experimentally measured values. It has been found that the fracture of the concrete observed at the macroscopic level is predominated by tensile damage at the mesoscopic level.