One of the objectives of the investigations documented in this thesis was an improvement of the evaluation of the wedge splitting test according to Tschegg with the help of numerical simulations. This wedge splitting test yields a specific fracture energy and a nominal notch tensile strength. The improved evaluation procedure enables the determination of Youngs modulus, the tensile strength and a corrected specific fracture energy. It is designed to be applied for brittle disordered materials like concrete and refractories. Due to this evaluation procedure no additional tests to determine Youngs modulus and tensile strength are necessary. A second goal of the thesis was to investigate possibilities to simulate crack initiation and crack localisation of brittle disordered materials in case of rather homogenous stress fields. For this purpose statistical distributions of strength and specific fracture energy have been applied. Shrinkage and cracking of a thin layer with perfect adhesion to the substructure was simulated. The crack spacing and the strain at crack localisation was investigated in dependence on the brittleness of the material, the applied constitutive models and the strength distribution. It could be observed that crack spacing and crack opening strain are mainly influenced by the strength distribution.