The phonon spectrum of cubic Si3N4 was calcd. by 1st-principles techniques. The results permit an assessment of important mech. and thermo-dynamical properties such as the bulk modulus, lattice sp. heat, vibration energy, thermal expansion coeff., and thermal Gruneisen parameter for this compd. The calcd. phonon spectrum shows a gapless spectrum extending to a cutoff energy of .apprx.1030 cm-1. The calcd. Raman- and IR-active phonon frequencies are compared with measured data in the literature.