The elastic, electronic and thermodynamic properties of the superconducting ErNi2B2C material at high pressure are investigated using the plane-wave pseudopotential density functional theory. The analysis shows the dependences of the elastic constants, bulk modulus, shear modulus, Young's modulus and elastic anisotropy factors on the applied pressure. The calculated electronic density of states (DOS) reveals that the DOS peak at the Fermi level (EF) will decrease noticeably with pressure. It can be concluded that the pressure may reduce the superconducting temperature (Tc) of ErNi2B2C since the relatively high Tc originates from the peak in the DOS. This phenomenon is also found in some other superconductors such as MgB2 and SrAlSi. Moreover, based on the quasi-harmonic Debye model, the results of the thermodynamic properties indicate that the pressure and temperature have significant influences on the thermal expansion coefficient and heat capacity.