The Russian gas market is highly regulated with low user prices of natural gas. In this paper we examine possible impacts of regulatory changes on the demand side of this market. In particular, we consider the effects on Russian energy consumers of increasing the regulated prices of natural gas, and how changes in Russian gas consumption may affect its gas export to Europe. We also examine the importance of Russian pipeline capacity to Europe, as well as impacts of hypothetical changes in Russian gas export behavior. For this purpose we use a detailed numerical model for the energy markets in Europe and Russia - LIBEMOD. Our results suggest that increasing the regulated natural gas prices will have substantial impacts on total consumption of gas in Russia, especially in the electricity sector. The magnitude of gas export to Europe will be significantly affected because more gas becomes available for export. Removal of other market imperfections in the Russian energy markets has smaller impacts on prices and quantities than imposing competitive natural gas prices. More competitive Russian gas export behavior would lead to much higher gas export to Europe, but our results suggest that Russian welfare would drop due to lower gas export prices.