Abstract: A two-phase random medium model is proposed to simulate the complex cracking process and failure mode of concrete. To represent the random distribution of mortar and aggregates of concrete, a newly developed two-phase random field is introduced to reconstruct the realistic concrete samples. The finite element and adjacent cohesive element, which can be considered as the potential cracking path, are generated for the numerical model. The complete cracking process and failure of concrete samples under uniaxial tension is proposed in the numerical simulations. By applying the two-phase random medium model, the main characteristics of concrete failure that cracks usually happen in the mortar rather than the aggregates can be well captured when the fracture energy of the aggregates are significantly larger than the mortar. The predicted stress-strain relationship agrees well with the experimental results, manifesting the validity of the proposed two-phase random medium simulation of concrete.