The need for social responsibility is now recognized by all organizations regardless of their size, location and legal form of organization. According to modern social responsibility is the responsibility of the organization for the impacts of its decisions and activities on society and the environment through transparent and ethical behavior. It contributes to sustainable development of society, including the care of his health and welfare. It also takes into account the expectations of stakeholders, meet the latest legislation and consistent with international norms of behavior, is integrated throughout the organization and practiced in its relationships. The present study considers how this concept can be implemented in practical activities of the organization. A model of social responsibility as a major factor of sustainable development of the organization and society as a whole, consists of four interrelated parts: social responsibility of government at every level of power, the formation of the social responsibility of a citizen, the formation of civil society and the allowable society stratification. Implementation of the proposed model is possible provided that will be elimination of the existing catastrophic economic, social and cultural stratification of society in Russia. It is necessary to introduce the model of «convergent economy», to eliminate the corruption.