The principal purpose of this paper is to investigate and probe the theories and methods of analytical solution and valid numerical solution for the zero-poles of the classical regular RC fractal fractance approximation circuits considering both the circuit structure specialities and mathematic representation characteristics.A brief survey and review on fractal fractance approximation circuits is given and new concepts of iterating circuit

iterating function

and iterating matrix etc are introduced.Finding the iterating matrix power by means of eigenvalue decomposition method or Hamilton-Cayley expansion

a simple expression of the analytical solution is derived for the normalized impedance function of some classical (such as the Oldham fractal chain

the Carlson fractal lattice

H-type

2h-type etc) fractal fractance approximation circuits.An analytical solution and a valid numerical solution for the zeros and poles of some classical fractal fractance approximation circuit are presented.The solutions are tested in both theory and simulation experiments.