Selecting a nuclear power plant site for power production and water desalination is a very complex problem, especially in countries with moderate technology. Many interrelated factors affect the process, and professional judgments by various experts are involved. Four sites, all located on the West Coast of Saudi Arabia along the Red Sea, were chosen as potential sites for building such a plant. (All sites were in either the northern or southern section of the coast; the central part was excluded for pilgrims’ safety.) The East Coast was completely eliminated in the initial screening process due to its strategic location, the existence of oil fields and refineries, and its proximity to other Arabian (Persian) Gulf countries (to minimize radioactive releases to these countries in case of an accident). A computer code based on Saaty’s eigenvalue technique and developed in a previous study was used in this analysis. Twenty-one main criteria were considered, and the sites were ranked to determine which was most desirable. Site 4 was found to be most suitable, followed by site 3.