The problem of finding unknown parameters in distributed parameter systems from the observations can be formulated as the equations of the first kind, whose solutions are not continuously dependent on the data. These problems are called non well-posed. The regularization or Tihonov's regularization is known as one of the stabilizing algorithms to solve non well-posed problems. In this paper we consider the regularization method for identification of distributed systems. Several approximation theorems are given for finding the solutions of equations of the first kind. Then, the identification problems are reduced to the minimization of a kind of quadratic functionals by using these theorems. On the other hand, it is known that the statistical methods for identification such as the method of maximum likelihood lead to minimization problems of certain specified quadratic functionals. Comparing these quadratic functionals, the relations between the regularization and the statistical methods are discussed.