Brittle materials are very complex in their behavior, which is characterized by anisotropy in tension and in compression. Therefore, numerical modeling of brittle materials requires an insight view of material behavior and an advanced constitutive material model. This paper presents an approach to model brittle materials by using the concrete damage plasticity model (CDP). Firstly, the CDP model, including the procedure to determine its parameters is described. Secondly, size effects due to tensile cracking and compressive crushing are considered within calibration of parameters and via development and implementation of a subroutine in ABAQUS. Finally, this numerical approach is validated through numerical simulation of different mechanical tests: three-points bending test, uniaxial compression tests.