Zirconium (Zr) alloy is a promising fuel cladding material used widely in nuclear reactors. Usually, it is in service for a long time under the effects of neutron radiation with high temperature and high pressure, which results in thermomechanical coupling behavior during the service process. Focusing on the UO2/Zr fuel elements, the macroscopic thermomechanical coupling responses of pure Zr, Zr-Sn, and Zr-Nb binary system alloys, as well as Zr-Sn-Nb ternary system alloy as cladding materials, were studied under neutron irradiation. As a heat source, the thermal conductivity and thermal expansion coefficient models of the UO2 core were established, and an irradiation growth model of a pure Zr and Zr alloy multisystem was built. Based on the user material subroutine (UMAT) with ABAQUS, the current theoretical model was implemented into the finite element framework, and the consequent thermomechanical coupling behavior under irradiation was calculated. The distribution of temperature, the stress field of the fuel cladding, and their evolution over time were analyzed. It was found that the stress and displacement of the cladding were sensitive to alloying elements due to irradiated growth.