In this chapter, theoretical studies regarding the design and analysis of silicon and SU-8 polymer waveguides are presented. The study starts with the design of single-mode optical wire waveguide at a transmitting wavelength of 1.55 µm. Effective index-based matrix method (EIMM) was used for this purpose, which is a two-step process. In the first step, effective index method (EIM) was used for vertical refractive index profile of waveguide, and then for the resulted lateral index profile, a transfer matrix method (TMM) was applied. The lateral mode profiles of wire for both transverse electric (TE) and transverse magnetic (TM) polarizations were also calculated using this approach. Bending losses of bend wire were computed using transfer matrix method along with conformal mapping technique.