Abstract: The behaviour of concrete can be simulated by the mesoscopic numerical model based on the finite element method and introducing the heterogeneity of materials. The relatively fine meshes of concrete would be practically impossible with the standard software, which are needed to reflect the geometry and properties of the aggregate, interfacial transition zone and matrix at the meso-level. In this construction, a mixed interface damage constitutive model is applied to develop a meso-structural model for simulating the fracture behavior of the concrete specimen loaded in uniaxial tension in 2D. Using the material mechanics method, the influence of the interfacial transition zone is smeared into a small region of the adjacent intact materials (aggregates and matrix). The elastic constants in the region are defined in terms of the constitutive properties of both the intact materials and the interfacial transition zone as well as the geometry of the homogenized domain. An elastic finite element program is employed as the basic stress analysis tool while elastic purely brittle damage mechanics is used to describe the constitutive law of a meso-level element. The maximum tensile stress is utilized as a damage threshold for all elements, especially for each material of composite elements. The numerical results show a good qualitative agreement with the macro fracture mechanism of concrete from experiment observations and illustrate the capabilities of the model.