Facility location models are usually employed to assist decision processes in urban and regional planning. The focus of this research is extensions of a classic location problem, the Weber problem, to address continuously distributed demand as well as multiple facilities. Addressing continuous demand and multi-facilities represents major challenges. Given advances in geographic information systems (GIS), computational science and associated technologies, spatial optimization provides a possibility for improved problem solution. Essential here is how to represent facilities and demand in geographic space. In one respect, spatial abstraction as discrete points is generally assumed as it simplifies model formulation and reduces computational complexity. However, errors in derived solutions are likely not negligible, especially when demand varies continuously across a region. In another respect, although mathematical functions describing continuous distributions can be employed, such theoretical surfaces are generally approximated in practice using finite spatial samples due to a lack of complete information. To this end, the dissertation first investigates the implications of continuous surface approximation and explicitly shows errors in solutions obtained from fitted demand surfaces through empirical applications. The dissertation then presents a method to improve spatial representation of continuous demand. This is based on infill asymptotic theory, which indicates that errors in fitted surfaces tend to zero as the number of sample points increases to infinity. The implication for facility location modeling is that a solution to the discrete problem with greater demand point density will approach the theoretical optimum for the continuous counterpart. Therefore, in this research discrete points are used to represent continuous demand to explore this theoretical convergence, which is less restrictive and less problem altering compared to existing alternatives. The proposed continuous representation method is further extended to develop heuristics to solve the continuous Weber and multi-Weber problems, where one or more facilities can be sited anywhere in continuous space to best serve continuously distributed demand. Two spatial optimization approaches are proposed for the two extensions of the Weber problem, respectively. The special characteristics of those approaches are that they integrate optimization techniques and GIS functionality. Empirical results highlight the advantages of the developed approaches and the importance of solution integration within GIS.