The performances of thermal-concentrated solar thermoelectric generators (TEGs) at three different geometric types are investigated numerically to aid in designing the practical devices. The temperature-dependent properties of the commercial thermoelectric material are taken into account, and an equivalent model based on the three-dimensional finite element scheme is developed to simplify and accelerate simulations. The constriction thermal resistance and thermal spreading resistance are considered in the equivalent model. Increasing substrate area increases the thermal concentration ratio; this improves the performance of the solar TEG. In the three geometric types, the smallest element with the substrate area of 90×90 mm2 provides the maximum system efficiency of 4.15%. For a TEG at a given element length, decreasing the cross-sectional area of the thermoelectric element is a feasible route to improve the performance. Under the situation of forced convection, varying convection heat transfer coefficient has an ignorable effect on the performance. For equal convective heat transfer coefficients, water cooling is better than air cooling for the net output power of the TEG because of its increased specific heat. Therefore, water cooling is recommended for the cooling of the solar TEG.