The program for the final disposal of low and intermediate level radioactive waste was established by Paks Nuclear Power Plant, Hungary. Preparation of final disposal has been done as part of a national program since 1993. The Central Nuclear Financial Fund and the Public Limited Company for Radioactive Waste Management (PURAM) have been established to coordinate organizations and activities for all tasks in connection, with nuclear waste treatment. The project was started with a geological screening in order to find the most suitable geological formation for a radioactive waste repository. The selected potential host rock is the Mórágy Granite Formation in the south-western part of Hungary, close to the village of Bátaapáti.This paper show and explain the results of an extensive study of the deformation and fracturing of Mórágy granite samples under uniaxial and triaxial loading conditions. In the investigation, the stress fracturing thresholds (crack initiation, crack coalescence and crack damage) were determined using stress-strain and stiffness curves without acoustic emission (AE) detection technique. Crack initiation was found to be best determined by the volumetric strain curve in both uniaxial and triaxial compression tests. As a detailed investigation, a comprehensive petrographical analysis using a petrological microscope was performed to identify the mode of cracking and the characterization of the cracking pattern.