The concrete was equivalent to a three-ingredient compound material, which was composed by aggregate, mortar and interface transition zone (ITZ). The random aggregate model was established using the Monte Carlo method. The relation between linear stress and crack was analyzed, which was used to describe the mechanics of concrete ingredients. The extended finite element method was used to simulate the failure response to various ITZ characteristics of concrete under uniaxial tension. With the tensile strength of ITZ increasing, the tensile strength, fracture energy and ductility of concrete are enhanced. The fractured modes are altered. The concrete’s elastic modulus increases with the elastic modulus of ITZ. With the thickness of ITZ decreasing, the tensile strength, elastic modulus and fracture energy of concrete increase. The interface thickness effect on concrete is reduced.