There is the GADM database where you can download Russian boundaries in a variety of formats suitable for QGIS and DIVA GIS where u can download data by country. Select and download free geographic (GIS) data for any country in the world.
Generalized political boundaries of the countries comprising the Former Soviet Union
Data formats: (Download data)
This is the data that comes from the MIT
For your reference : here is the information to ensure you get the right shapefiles
A good general source for map data, including, but not limited to the political boundaries of the nations of the former Soviet Union, is Natural Earth.
Boundaries of nations and nation-like things are under the "cultural" category, and can be downloaded at a variety of resolutions (1:10,000,000; 1:50,000,000; 1:110,000,000) and a variety of ...