Abstarct: Facility location problem is one of the most important fields of operation research that is used to model real problems such as locating hospitals, firefighting stations, banks, emergency centers and etc. However the existence of uncertainty and ambiguity are unassailable in real situations and in most of the times it is not possible to determine the value of parameters certainly and exactly. To model real problems in such cases, a proper method is used to model these ambiguity and uncertainty. The fuzzy set theory is an efficient tool to model vagueness and uncertainty of real problems in mathematical forms. This theory is able to model uncertain and ambiguous concepts, variables and systems in mathematical form and provide the situations to reasoning, conclusion, control and decision making in uncertainty. Hence it is so important to studding of fuzzy facility location problems. In this thesis the crisp version of p - median and p center problems are defined and the fuzzy form of 1 - median, 2 - median and 1 - center problems are studied. Some previous existing methods are explained. Also some new efficient methods are proposed to solve these problems. More over continuous facility location problems with square of Euclidean norm and L_1 norm are discussed and some new methods are presented to solve them.