For a round shaped heat source or heat sink, annular thermoelectric couples (ATCs) are designed to remove the contact thermal resistance induced by geometrical mismatching. In this study, the performance (power and efficiency) of ATCs subjected to a constant heat flux condition, which is often encountered in the utilization of solar energy and radiant heat, was assessed by a developed theoretical model. A finite element method was used to incorporate the temperature-dependence of thermoelectric materials and Thomson effect. The effect of annular shape parameter S-r, a parameter characterizing the geometric feature of ATCs, was particularly stressed. Also the influences of external load, heat flux, heat transfer capability at the cold junction and leg height were analyzed. The performance comparisons with the condition of constant temperature were conducted. Results show that the influence of Sr is not affected by other parameters. Contrary to a constant temperature condition, the performance enhances with Sr deviating from 1 (i.e., flat-plate thermoelectric couple), and the power increases with an increase of leg height. The external load maximizing the performance is larger than the internal electrical resistance. The larger the heat flux is, the better the performance is. As the heat transfer capability at the cold junction increases, the performance reduces, first sharply and then leveling off. Since the performance of ATCs is superior do FTCs and the undesired contact thermal resistance can be eliminated by the use of ATCs, the potential of ATCs is demonstrated.