The environmental conditions and the geological and tectonic features of rift zones on the Arctic shelf of eastern Siberia were analyzed using information obtained from field studies as well as model calculations.For the rift zones, a tectonic model is suggested in which the properties of the shelf sediments were considered. A paleogeographic scenario is proposed for the formation of negative neotectonic structures in the area. On the basis of the paleogeographic scenario and the suggested model, a mathematical simulation of the long term dynamics of permafrost and the gas hydrate stability zone on the shelf has been performed for the last 400.000 years.As a result of the long-term evolution of permafrost within the rift zones, pocket-like (dome-shaped) structures similar to anticlines have been formed at the base of permafrost as well as open endogenic subsea taliks. It is assumed, that the anticlinal structures act as traps for sub-permafrost gases and their hydrates, whereas the open taliks serve as channels for their emission.With the results obtained it is possible to predict the conditions of formation of anticlinal traps and open taliks in the rift zones and their relation to the periodical drying or submergence of the shelf.