Extremely thin nanowires (NWs) would bend during the heteroepitaxial growth process. This phenomenon can increase the emission intensity due to the strain fields within bent NWs. Although the growth mechanism of NW heterostructures has been widely studied in theory, the theoretical studies are centered on growth on the surface of straight NWs, and the bending mechanism on extremely thin NWs has not been clearly explored. In this contribution, we have established an analytical thermodynamic theory to study the mechanism of bending induced by heteroepitaxial growth on the surface of thin NWs. It is found that the balance between surface energy and elastic strain energy plays a crucial role in the determination of the bending of NWs. The strain relaxation energy induces bending of NWs with small radii and high deposited amounts, while the size-dependent surface energy becomes more significant and restrains the bending of NWs with large radii and low deposited amounts. The established theoretical model not only explained the bending mechanism of NWs but also provided useful information to design the epitaxial growth on the surface with a nanoscale curvature.