This article examines the problems of taxation of income of foreign digital companies faced by tax administrations worldwide, including the Russian Federation. The subject of this research is the current models of taxation of income of foreign digital companies in Russia and the world. The goal consist in the development of new approaches towards administration of tax income of foreign digital companies in the Russian Federation for the long-term, as well as to ensure country's fiscal interests in the immediate future. Within the framework of this research, the author reviews the modern concept of permanent representation of foreign company, and determines the reasons impeding the implementation of this concept in the area of e-commerce. Assessment is given to feasibility of introducing digital tax in Russia. The scientific novelty consists in the author’s original concept of establishment of permanent representation of foreign digital company, as well as in proposal for its implementation into the tax system of the Russian Federation. Recommendations are also given on introduction of digital tax in Russia, including formulation of its basic elements, such as the object of taxation, tax base, tax rate, tax period and tax breaks. In the conditions of limited open analytical data on transboundary e-commerce on the territory of the Russian Federation, the author estimates feasibility of introducing digital tax and its economic effect on the country.