First-principles density functional theory calculations have been performed to investigate the structural, elastic and thermodynamic properties of rubidium telluride in cubic anti-fluorite (anti-CaF2-type) structure. The calculated ground-state properties of Rb2Te compound such as equilibrium lattice parameter and bulk moduli are investigated by generalized gradient approximation (GGA-PBE) that are based on the optimization of total energy. The elastic constants, Young’s and shear modulus, Poisson ratio, have also been calculated. Our results are in reasonable agreement with the available theoretical and experimental data. The pressure dependence of elastic constant and thermodynamic quantities under high pressure are also calculated and discussed.