Abstract: The three-gradation concrete is taken as a three –phase composite consisting of mortar matrix, aggregate and bond between matrix and aggregate, and the cracking process of the three-gradation concrete beam specimen under static and dynamic loadings is analyzed with nonlinear finite element method at micro-scale level. The aggregates, following a predefined size distribution, are placed randomly in the specimen. The shape of the aggregates is approximated by circles and their minimum diameter is 12.5mm. Nonlinear constitutive relations are proposed to model cracking, softening, yielding and crushing of the composites. The full curves of stress and strain at the key location of the beam are given, and the results are also compared with that of homogeneous materials. The results from numerical simulation show that mechanical behaviors are directly related to the microstructure of concrete, and the interface is the weakest location where cracking usually occurs first. The failure process of concrete reveals that the phenomenon of tensile strain softening and localization is obvious, and the results of numerical analysis are very close to those of experiments.