Mechanical behavior of structures made from cementitious materials has been successfully modeled using non-linear fracture mechanics in recent decades. On the structural scale, an assumption of homogeneity of the material is valid and well established theories can be applied. However, if focus is put on phenomena of a similar scale as is the characteristic size of inhomogeneities of the material, a model which re ects the heterogeneous nature of the material needs to be applied. This is, indeed, the case for prediction of mechanical properties of a material based on the knowledge of properties of its constituents and composition or when focus is put on a single crack and an accurate estimation of its width. Similarly, in the case of ordinary portland cement paste, a simple relationship linking the strength of the cement paste with its porosity was proposed and widely used for a long time. However, in today's blended cements, systems with higher porosity and higher strength at the same time are often found. Thus, the arrangement of the phases in microstructures plays an important role. These microstructures are highly heterogeneous and a model for prediction of mechanical properties of the materials needs to be able to take this complexity into account. In this thesis, two frameworks for prediction of strengths of cementitious materials are developed. The rst one relates the strength of materials with aggregates with the properties of the matrix and distribution of aggregates. The second one relates the strength of cement paste with the properties of cement phases and its microstructure. The frameworks consist of an experimental part, an identication of material properties from the experiments and a modeling part based on an approximative discrete particle model. In the case of mortar and concrete, it is demonstrated that the measured mode-I fracture properties of the matrix together with tted ratios of mode-I to mode-II properties are sucient to provide estimations of mode-I, mixed-mode and compressive experiments matching favorably experimental records. In the case of pure cement paste, it is experimentally observed and numerically veried that the cracking plays an important role in mode-I as well as compressive experiments. The approximative particle model extended for materials with heterogeneous matrices predicts strengths matching favorably experimental records in a qualitative way.