The article is devoted to social innovations as new solutions and approaches to solving problems in the social sphere. Core features of social innovation are introduced on the theoretical level. Due to certain characteristics of the third sector organizations they have better opportunities to introduce innovative changes and improve efficiency of decisions than private or governmental sectors. Third sector organizations are considered to be most promising actors as they create feasibility and subsequent diffusion of new ideas and approaches initiated by citizens. The empirical base of the analysis includes surveys of Russian federal elites in 2008 (n = 303), 2011 (n = 300), 2013 (n = 300), 2014 (n = 300) years; the all-Russia population survey (18+) in 2014 (n = 1500). The results received demonstrate the presence of a pronounced social demand for increasing the role of non-profits in providing social services. Both the population and elite groups expressed such a demand. However, the current impact of non-profit organizations’ participation in providing social services was evaluated below average by all groups of respondents. The article concludes that there are growing expectations of non-profits’ contribution in providing social services and evidences of a legitimate request from the government for outsource social services to non-profit organizations.