Thermoelectric materials are capable of direct conversion of thermal energy to electrical energy and vice versa. Their applications include thermoelectric coolers, generators, as well as sensors. Conventional thermoelectric devices consist of multiple units of p-type and n-type semiconducting elements, in which electrical current and heat flux flow parallel to each other. In contrast, transverse thermoelectric devices could decouple electrical current and heat flux such that they flow perpendicular to each other. Transverse thermoelectricity could be realized in single-phase anisotropic materials or composite materials with engineered anisotropy. Studies have shown that composite transverse thermoelectric materials could provide a better performance than their single-phase counterparts. In this dissertation proposal, two configurations of transverse thermoelectric composites are examined using both analytical and numerical methods. Mathematical models are established to calculate the effective properties of anisotropic thermoelectric composites by analyzing the representative unit cells using the Kirchhoff circuit law (KCL) and the Thevenin’s theorem followed by tensor transformation. Thermoelectric figure of merit (ZT), power factor, as well as cooling performance (maximum cooling temperature ΔTmax) of transverse thermoelectrics are studied. Comparisons between the mathematical models and numerical simulation showed good agreement, while some discrepancies are observed and discussed. Since transverse composite thermoelectrics can decouple the electrical and thermal transports, they can offer new opportunities for device design including thin film sensors and cascading coolers, as well as for performance enhancement such as improved power factors. / Mechanical Engineering