The paper discusses social aspects of higher education institutions engagement with their regional communities. On the basis of the cases of the Russian Siberian and Southern Federal Universities the author analyzes practices and formats of their interaction with different regional stakeholders as part of the FUs' social function implementation. The FU's capacity to enhance their third mission is assessed. The author suggests a set of indicators to assess universities social activities impact on development of the regions, and puts forward recommendations on building the federal universities capacity for fulfilling their third role. The paper is prepared within the framework of the Ministry of Education and Science project "Organizational and analytical support to the national priority project "Education" on activities aimed at "Development of Federal Universities", carried out by the National Training Foundation.