Using the structural parameters and the elastic stiffness constants reported in the literature (by Guo et al. in Solid State Commun., 340, 114488 (2021)) as well as different appropriate analytical and semi-empirical expressions, we reported the high compression effect up to pressure of 27.8 GPa on the average sound velocity and Debye temperature θD of cubic rocksalt calcium telluride (CaTe) semiconducting compound. The pressure dependence of the Debye temperature θD for CaTe compound was obtained using two different approaches. We found that both the average sound velocity and Debye temperature of CaTe compound increase monotonously and non-linearly with enhanced pressure up to 27.8 GPa. We note that similar behavior on the average sound velocity and Debye temperature θD was also observed in the literature for the same compound and for other materials with different crystallographic structures. The deviations on θD between the two different approaches and to those of the literature are quite large at high pressures.