The authors analyse the intra-industry trade with an identical product. Their analysis is based on models of Brander (1981), and Brander - Krugman (1983). They are concerned with the international duopoly created after liberalizing of economies of two countries, in which the industries producing analyzed product are local monopolies. The authors show why both local monopolists are invading into the foreign markets and present consequences of resignation of such an invasion. They also discuss conditions under which trade with an identical product is social beneficial for both trading countries. The authors show that in the model with zero transport (or transaction) costs the bilateral intra-industry trade with identical product is beneficial for both countries. However by transport (transaction) cost greater than zero, there is a marginal transport cost, after achieving which trade wouldn't be beneficial any longer.