Russia is one of the key players in the Arctic due to its significant hydrocarbon resources, and the relevance of developing its Arctic offshore deposits is obvious. However, the presence of considerable reserves of oil and gas on the Russian Arctic shelf does not guarantee the success of projects aimed at developing these deposits, since a whole group of contradictory political, macroeconomic, and other factors impacts their initiation and realization. This influence has now intensified with the current problematic macroeconomic situation in Russia, particularly in the energy sector. Furthermore, the current international political scene has a direct impact on Russia’s activities in the field of offshore projects. Economic, geopolitical, climatic, infrastructure, ecological, and other factors create uncertainty in the development of the Arctic oil and gas projects. The development of Arctic territories and shelf deposits, as part of a complex economic system, is subject to numerous disputes. The purpose of this paper is to study the prospects for the implementation of projects for the oil and gas production from offshore Arctic fields. As a result of the research, the work presents a methodology for assessing the prospects of the Arctic oil and gas offshore project which is called TESCIMP methodology. It is based on the TESCIMP analysis, a two-dimensional classification of TESCIMP indicators and the algorithm for selecting TESCIMP factors used in the analysis of specific deposits and choosing one of the projects for its development as the most promising.