The Black Sea coastal zone of the Caucasus can recently be considered as one of the fast developing regions in Russia. Agriculture, transportation, oil industry, and tourism are among the most pronounced activities constructing the local economy and affecting the migration of population. The region is exposed to various natural hazards – floods, debris flows, snow avalanches being reported several times per year. Despite almost half century research in the field of the natural hazards risk in Russia, the world-wide accepted concept of risk is still hardly considered by the state and the local authorities in determining the priorities in possible natural hazards-related losses decrease and in developing of the required mitigation measures. With debris flows and snow avalanches as the examples of the natural hazards, we present the results of the social and economic risk estimation at the Black Sea coastal territories of the Caucasus. In general, the individual risk in here varies from acceptable to allowable from area to area. The maximal values of economic risk are estimated for the Adler region (more then 1 mln. rub. per year).