A numerical code MFPA~(2D)(material failure process analysis) was used to model the crack initiation and propagation in reinforced concrete bridge pier,which were subjected to eccentric loading.A certain statistical function was introduced to reflect the concrete heterogeneity.The elastic damage constitutive law with residential strength and the elements mechanical properties reducing method were used.The load-displacement response and crack propagation processes simulated with this code show that there is a good agreement with those observed in experiments.It was found that the fractures developed in the concrete observed at the macroscopic level are predominant by tensile damage at the mesoscopic level.The stress distribution curve and the failure process of the sample are reported in this paper.Through picking up two multiple elements information lines from the tensile area,which provide the stress changing information at the different position with the loading step,the structure failure mechanism is displayed which give a basis for the study of the failure process in reinforced concrete under loading and the design of mechanics properties for the reinforced concrete.