Abstract
This work introduces one-dimensional numerical application of an elastic and isotropic half space in which the governing equations have been taken in the context of the two-temperature thermoelasticity without energy dissipation theory to show the effects of the two-temperature parameter on all the studied fields and to stand on the contributions of this theory. The results of this work confirmed that the two-temperature thermoelasticity without energy dissipation is valid when the thermo-dynamical temperature and the temperature of the heat conduction are not coinciding.