  We have investigated the structural, electronic, mechanical, phononic, and
superconducting properties of the Zr$_2$Ir compound with a body-centered
tetragonal crystal structure using first-principles calculations. Our analysis
reveals that the Zr$_2$Ir compound shows mechanical and dynamically stable by
using with and without spin-orbit coupling (SOC) effect. After calculating some
properties such as elastic constants, Bulk modulus, Young's modulus, Poisson
ratio, Debye temperature, and sound velocity, we found that Zr$_2$Ir is
ductile. When the elastic constants $C_{11}$ and $C_{33}$ are compared, it is
determined that the situation changes in the opposite direction under the
effect of SOC, that is, more compressibility along the x-axis turns into the
z-axis. Here, the electronic band structure and intensity of the states
calculated for the compound show a metallic character. The superconducting
critical temperature ($T_c$) and electron-phonon coupling constant ($\lambda$)
were found to be 7.50 K and 0.93 without SOC and 7.62 K and 0.96 with SOC,
respectively. We determined that although the Zr$_2$Ir compound has a strong
electron-phonon coupling regime, the inclusion of SOC slightly reduces its
critical temperature and electron-phonon coupling constant.
