The fracture mechanical properties, in particular uniaxial tensile strength ft, Young’s modulus E0 and fracture energy GF as well as the shape of the stress-strain and the stress-deformation relations were investigated for high-strength and normal strength concrete. In order to analyze failure mechanisms of these concretes, the roughness and the fractal dimension of the entire fracture surfaces and of their components (fractured aggregate, cement paste and cement paste-aggregate interface) were calculated. These data showed a clear correlation with fracture properties of the concretes investigated. Further, the mechanisms of the transfer of tensile stress across the crack were studied numerically. Hereby, a new method was applied to generate artificial concrete failure surfaces with a given fractal dimension. The results of the FE simulations confirmed the experimentally found correlations between the condition of the failure surface and the fracture mechanical properties of the investigated concretes.