In this paper, we deal with competitive facility location problems in which the demand of each customer depends on the facilities. In our models two competitive companies intend to locate their facilities on the market in order to maximize the total demand acquired from the market. The distances between the facilities and the demand points are measured by
rectangular distance. At first we consider the linear model and derive the optimal policy for locating the facilities. We then extend the model to planar case and also derive the optimal policy.