The results of research aimed at predicting the evolution of structural-tectonic blocks of the Earth's crust for selecting Storage Sites of High Level Radioactive Waste (HLRW). The multifactorial structural-tectonic model of Nizhnekansky Granitoid Massif (NKM) was developed, as the most probable burial site of HLRW in Russia. The synthesis of methods of analysis of geological-geophysical data, paleotectonic reconstruction of stress and modeling of stress fields expand the area of predicting stability of geological environment thus providing the capability to make a more accurate assessment of its destruction during a long period of radiobiological danger of HLRW. As it was shown, blocks with high level of concentration of intensiveness of stress are potentially hazardous in relation to development of tectonic destruction.