Abstract: In this dissertation, a scattering field Transmission Line Modeling (TLM) method is developed to calculate electromagnetic scattering of three dimensional homogeneous gyrotropic objects, which are anisotropic, non-reciprocal and highly frequency dispersive. First a single-frequency three dimensional TLM algorithm is established to obtain bistatic radar cross sections of gyroelectric and gyromagnetic spheres, cubes and finite circular cylinders, where the permittivity and permeability tensor elements are constant values. For verification, the results for gyrotropic spheres are compared with those from previous studies, in which an analytical approach and the Method of Moments along with the Conjugate Gradient Fast Fourier Transform method were used. Next, one dimensional and three dimensional TLM algorithms for frequency dispersive gyrotropic material modeling are developed. Reflection and transmission coefficients of gyroelectric and gyromagnetic slabs are calculated from one dimensional TLM simulation numerically and compared with analytical solutions, which are also described in this dissertation. Radar cross section results of the frequency dispersive three dimensional scattering field TLM algorithm are compared with those of the single frequency method by simulating a sphere, a cube, and a finite cylinder, all gyromagnetic. The Z transformation is applied to implement the convolution operations, originated from the frequency dependent parameters of the gyrotropic media. We used the discrete Fourier transform to obtain frequency domain responses from transient time domain simulation results. Finally, radiation properties of a Hertzian dipole in the presence of a finite gyromagnetic substrate are studied, simulating the structure for three special cases, where the dipole is directed along each of the three coordinate axes in turn. The near field to far field transformation is adapted to the three dimensional TLM algorithm in order to overcome the handicap of truncated computation space.