Abstract: In this paper, a method for evaluating the coefficients of the rational fraction ap proximation of transfer functions with prescribed phase-frequency or magnitude-frequency curve over a finite frequency range is presented. It is based on the modified method of least squares, i.e. to minimize the weighted sum of the squares of the errors, in order to avoid to solve the system of non-linear algebraic equations by using the ordinary method of least squares. The evaluation of the optimum coefficients is then reduced to solving a system of linear algebraic equations, which can easily be done by using electronic digital computers. A numerical example is given for illustration.