Abstract The main goal of this article is to contribute to the theoretical analysis of international trade under imperfect competition using the Cournot oligopoly model with heterogeneous firms. In particular, our objective is to provide some insights into the role of cost asymmetry in studying the effects of trade liberalisation in the Cournot oligopoly framework. In order to introduce firm heterogeneity into the oligopoly model we use the generalised Cournot framework with asymmetric firms that differ in terms of their productivity, levels of output and market shares. We show that trade liberalisation leads to the elimination of less productive firms and results in lower equilibrium prices, higher sales per firm and lower markups in the industry.