We show that the classic Hotelling’s model of spatial competition between two players with linear transport costs (1929) has the price equilibrium solution for all locations under the assumption that duopolists secure themselves against being driven out of the market by ndercutting. In order to formalize this natural logic of player’s behavior we employ the concept of the equilibrium in secure strategies (EinSS) as the generalization of the Nash-Cournot equilibrium. Existence and uniqueness of the equilibrium solution of the price setting subgame allows to obtain the complete solution of the two-stage location-price Hotelling’s game. The obtained results are interpreted and further research is discussed.