Abstarct Facility location is one of the most important problems in strategic decisions of private firms and governmental organizations. Covering problem is one of the most useful problems in the field of facility location. In this thesis, two new models in the field of covering problems in continous space are presented. The first model is called Continous Set Covering Problem (CSCP) which is based on a continous two dimentional space instead of network space, with the aim of minimizing the number of located facilities, so that all customer points will be covered. The second model is called Continous Set Covering Problem with Demand (CSCPD) which adds customer demands and capacity of facilities suppositions to the first model, with the aim of minimizing the number of located facilities, so that the demand of all customer points will be fully covered. These two models are in the form of mixed integer nonlinear programming (MINLP). Using an innovative approximation, the models will be converted to the form of mixed integer linear programming (MILP). A three step heuristic algorithm called Compass is presented to solve the CSCP model. This heuristic algorithm is based on a theorem according to it, customer points that have a joint covering zone, are palced in distinct sets and each set is assigned one facility. The heuristic algorithm is validated by solving 20 random sample problems with different dimensions and comparing its solutions with the GAMS software solutions. Average of difference between the final goal value of heuristic algorithm and GAMS software for the sample problems with dimensions up to 50 customer points with 2650 variables including 2550 binary variables and 40100 constraints is equal to about 3% and this shows that the heuristic solutions are close to optimal solutions. Solving time for the heuristic algorithm is much less than GAMS software, so that the heuristic algorithm solves problems with dimensions up to 300 customer points with 90900 variables including 90300 binary variables and 1440600 constraints in a time duration which is about 50 seconds. Unlike the GAMS software presents only one point for each customers set, the heuristic algorithm presents several candidate point to locate the facilities, and this gives more alternatives to decision maker to choose the location points.