Synthesis of RC distributed networks is considered in this thesis. The behavior of these networks is formulated as a differential equation in terms of impedance. Using this behavioral equation and a boundary condition, an optimization problem is constructed so as to yield a solution that approximates a specified impedance characteristic. The technique is demonstrated for several example network configurations. By assuming an initial structure, a gradient algorithm is employed to solve the optimization problem. Two S-plane representations of the impedance, one along the oj-axis and the other along the a-axis, were used in the solution. Both representations afforded rapid convergence, with the o-axis examples achieving more accurate structures in less time. These examples clearly demonstrate the effectiveness and practicability of this method.