In this contribution, the Discretized Mie-Formalism (DMF) for plane wave scattering by irregularly shaped objects is presented in both cylindrical and spherical co-ordinates. Besides the direct method we discuss an iterative procedure which results in less computational effort and a higher numerical stability. This makes the DMF applicable to aspect ratios and size parameters which have only been treated by use of the Extended Boundary Condition Method so far. The iterative DMF is a Method of Moment scheme applied to the continuity condition of the tangential electromagnetic field components at the scatterer surface. Based on the differential equation formulation, the DMF can be considered to be the numerical generalization of the Mie theory to particles with non-spherical boundaries. By use of a special Finite Difference technique, the so-called Method of Lines, the Helmholtz equations for the Debye potentials, related to the scattering process, can be transformed into an uncoupled system of ordinary differential equations depending only on the radial coordinate. This system can be solved analytically by taking the radiation condition into account. In this way, the final calculation can be restricted to the surface of the scatterer as known from surface integral approaches. Additionally, a decoupling of the orientation of the scatterer with respect to the incident field from its geometrical and physical configuration is achieved. The theoretical description is completed by an application to scatterers with different shapes, and in different size parameter regions.