Abstarct: This thesis considers the location problem of a circle in the plane. In the first chapter, firstly, a brief story of the location problem is noted, next, an introduction to the problem is presented. Primary definitions and concept are explained. In chapter 2, initially, we discuss about the polar set and then a number of features of block norms are defined and we notice some of special block norms such as Manhattan, Tchebycheff and One-infinity. In this chapter, the relation between block norms and the shortest path also is discussed. In chapter 3, we will focus on the analysis of the circle location problem with objective function of the least squares. In other words, we will find a circle such as to minimize the sum of the distance squares of the given points. Also, in this chapter, an approximation method is introduced to solve the problem. At the end of the chapter, presented methods are compared with each other by giving an example. In chapter 4, we will consider the circle location problem with the objective function of minimax. In other words we look for a circle in which the maximum distance of the given points to the circumference is minimum. In this chapter, a situation is discussed in which the distances in a plane are measured with block norm and then we will present the programming model which is equal to it. At the end of the chapter, afew of examples are solved with different block norms. In chapter 5, a study is conducted about the circle location ploblem with the objective function of the minisum and Euclidean norm. In other words, we will find a circle such that the sum of the weighted distances between the given points and circle is minimum. In this chapter, we will introduce lemma which identify the center of the optimum circle. An algorithm is presented to find the center of the optimum circle. In chapter 6, disk location problem with the objective function of the minisum and the block norm are studied. In the first part, we note the result which go true for all functions of arbitrary norms, and in the second part, we confine our study to the block norms. In the second part, we will concentrate upon lemma helping to identify the center of the optimum disk. In the third part of the chapter, a programming model is presented for the location problem of the block norms and as in special cases for Manhattan and Tchebycheff.