Rhenium is an important material for research and engineering applications due to the high bulk modulus, high melting point and excellent creepresistance. Theresponse of the shear elastic constant C44 of rhenium to temperature and pressure is important to the design and application of rhenium and its alloy. Raman scattering technique has unique advantages in studying the shear elastic constant C44 of hexagonal closest packed (hcp) metal under different temperatures and pressures. However, it is difficult to obtain the signals of low wavenumber Raman scattering for hcp metals due tothe strong reflection and shallow penetration depth of metals, especiallyunder a certain temperature and pressure loading. In this work, the lateral-incidentRaman scattering technology was carried outtoreduce the influence of metal strong reflection on Raman spectra. Consequently, we successfully measured E2g modes of polycrystallinerhenium under different pressure and temperature. The shear elastic constant C44 is 133 GPa at ambient condition. And we obtainedthe response of the shear elastic constant C44 of rhenium to temperature and pressure. The results show that the elastic shear coefficient C44 of polycrystalline rhenium increases with the increase of the pressure, and decreases with the increase of temperature. And, this work proposes a good research method for the shear elastic constant of metal material with Raman scattering.