Zirconium (Zr) alloy is the core component of nuclear power reactor with small thermal neutron absorption cross section, excellent corrosion resistance and mechanical properties. Its mechanical behaviors play a key role in the safe operation of the reactor under service conditions. The elastic modulus is one of the crucial mechanical properties of Zr alloy, which affects the elastic-plastic deformation. The formation of voids by irradiation and the solid solution effect of fission fragments will affect the elastic modulus of Zr alloy, thereby altering the mechanical behaviors. Based on density functional theory, phase field micro-elasticity theory, and elastic self-consistent, this work has revealed the influence of the fission fragment elements and irradiation voids on the Zr elastic modulus. The quantitative relationship model has been established between the elastic modulus and the changes in irradiation damage dose and temperature, further promoting the research and development in the mechanical behaviors field of Zr alloy irradiation.