This work presents a generalized analytical method to obtain the S and Z matrices for irregular shaped planar resonant structures commonly found in mixed signal circuits. The method is based on a segmentation technique that uses an interconnect matrix in conjunction with a cavity model where resonant modes are predicted accurately through closed form expressions. The analytical formulation is very versatile and can be applied to both digital and RF circuitry. Typical structures such as the L-shaped power plane, rectangular ring power plane and rectangular coil inductor are considered where the S and Z matrices have been compared with published literature and full wave solvers. In all cases, there is excellent agreement. A design methodology has been developed to shape the power planes so that no resonances occur within the frequency range of interest. In the case of inductors, a similar design methodology can be developed where a physical layout is obtained for a required inductance value.