Annular thermoelectric generators can eliminate the thermal contact resistance formed due to geometry mismatch when flat-plate thermoelectric generators are used with round shaped heat source or heat sink. Therefore, in this study, the numerical simulation of a segmented annular thermoelectric generator (SATEG) is investigated using three-dimensional finite element analysis. The thermoelectric and mechanical performance of the segmented annular thermoelectric generator is studied by considering temperature dependent thermoelectric material properties and elastoplastic behaviour of copper and the welding layer (solder). The influence of segmented pin geometry on the performance of the segmented annular thermoelectric generator is investigated and comparison is made with non-segmented annular thermoelectric generators. COMSOL 5.3 Multiphysics software is used to investigate the effects of heat source temperature, thermoelectric leg length and leg angle on the electrical and mechanical performance of the segmented and non-segmented annular thermoelectric generators. Results show that the segmented annular thermoelectric generator has a greater efficiency compared to the annular thermoelectric generator (ATEG) with Bismuth telluride material when the temperature difference is greater than 100 K. In addition, the efficiency of the SATEG is found to be 21.7% and 82.9% greater than that of the Bismuth telluride ATEG and Skutterudite ATEG respectively at 200 K temperature difference. Finally, the results show that increase in thermoelectric leg length can reduce the thermal stress and electrical performance of the segmented and non-segmented thermoelectric generators. Results obtained from this study would influence the design and optimization of segmented annular thermoelectric generators.