The structural phase transition and elastic properties of BeTe are investigated by first-principles calculations using pseudopotential plane-wave method within the generalized gradient approximation. The calculated structural parameters of BeTe are consistent with previous experimental and theoretical results. According to the enthalpy and pressure data, it is predicted that the pressure value in the phase transformation from B3 to B8 is 35.88 GPa, which is well in line with the experimental data of 35 ± 5 GPa. Especially the elastic constants of B8 under high pressure of BeTe are studied for the first time, from which the elastic moduli, compressional and shear wave velocities as well as Debye temperature as a function of pressure are analysed successfully.