Nowadays, the use of thermoelectric semiconductor devices are limited by their low efficiencies. Therefore, there is a huge amount of research effort to get high thermoelectric efficient materials with a fair production value. To this end, one important possibility for optimizing a material’s thermoelectric properties is reshaping their geometry. The main purpose of this thesis is to present a detailed analysis of thermoelectric efficiency of 2 lead systems with various geometries in terms of linear response theory, as well as 3 lead nanowire system in terms of the linear response and nonlinear response theories. The thermoelectric efficiency both in the linear response and nonlinear response regime of a model nanowire was calculated based on Landauer-B¨uttiker formalism. In this thesis, first of all, the electron transmission probability of the system at the hand, i.e. 2 lead or 3 lead systems are investigated by using R-matrix theory. Next, we make use of these electron transmission probability of model systems to find thermoelectric transport coefficients in 2 lead and 3 lead nanowires. Consequently, the effect of inelastic scattering is incorporated with a fictitious third lead in the 3 lead system. The efficiency at maximum power is especially useful to define the optimum working conditions of nanowire as a heat engine. Contrary to general expectation, increasing the strength of inelastic scattering is shown to be a means of making improved thermoelectric materials. A controlled coupling of the nanowire to a phonon reservoir for instance could be a way to increase the efficiency of nanowires for better heat engines.