In this study, we have developed a three-dimensional finite element method for solving the equations of electrical and thermal flows. The 3D analysis of bulk material and wire array element was demonstrated, and electrical potential and temperature distributions were calculated in thermoelectric elements of bulk bismuth and wire array structures for various boundary conditions. The influence of wire array structure on effective thermal conductivity of the element was discussed in this study. It was clarified that thermal exchange between bismuth wire and glass template in wire array element plays a very important role for reduction of thermal conductivity.