Radio wave absorbing materials (RAM) are commonly found amongst high-tech products such as LCD electronic devices, laptop and desktop computers. Electromagnetic wave absorbing materials are composed of dielectric materials mixed with ferrite, a magnetic material, with varying shapes and sizes. It should be capable of absorbing electromagnetic energy at normal and large incident angles over a wide range of frequencies. This requires the material to possess a large relative complex dielectric constant (permitivity £`r), as well as a large relative complex magnetic permeability constant (£gr). Due to the nature of the complexity of the RAM, which surpasses standard analysis techniques, we have derived, for this thesis, frequency-domain two-dimensional finite-difference formulas for modeling the electromagnetic behavior of RAM. This involves using a material that has a given £`r(1:10 range) and £gr(1:1000 range) which covers a vast range of indices of refraction. To reduce the computational domain, we took care of implementing the numerical absorbing boundary conditions, while also implementing material averaging schemes for the finite-difference coefficients that cover the region where sample medium changes. Simple numerical examples are included to verify our mathematical model. We also implemented an optimal one-dimensional multi-layered RAM design, designed by using a constrained optimization searching technique. Included in the thesis are two complete, practical, optimal designs considering available material parameters (finite loss tangent) as well as their actual manufacturing limitations (layer thickness).