Using this matrix and initial data, obtained by the recognized international organizations we have developed the mathematical model that gives the opportunity to calculate the components of human life quality and safety as the components of sustainable development index and harmonization level of this development for every country. The system of indexes and indicators has been developed and gauging matrix for sustainable development processes (SDGM) in 3 dimensions: economic, ecological and socio-institutional has been offered. The global modeling of sustainable development processes for the large group of the countries in terms of human life quality and safety has been performed. The results of modeling have been explained in details by every dimension of the sustainable development.