The high-temperature lattice constants and elastic moduli of the silicon nitrides are calculated using the plane-wave pseudo-potential method combined with the vibrational Debye-like model. β-Si3N4 is ductile at low temperature and brittle at high temperature. γ-Si3N4 is found to be brittle and covalent in nature. We find a positive slope of the β→γ phase boundary, hence, at higher temperatures it requires higher pressures to synthesize γ -Si3N4. The α → γ phase boundary may be expressed as P=16.29-1.835-10-2 T+9.33945-10-5T2-2.16759-10-7 T3+2.91795-10-10T4. We also obtain the electronic structures and energy bands of Si3N4 with and without pressure. The interaction between Si-s, p and N-s, p plays a dominant role in the stability of α-Si3N4. The α- and β-Si3N4 have the ΓV-ΓC indirect band gaps (4.9~eV and 4.4~eV) while γ-Si3N4 has a direct band gap(3.9~eV). The tops of the valence bands for α- and β-Si3N4 are along the Γ-M and Γ-A direction, respectively. Our results are consistent with the experimental data and the theoretical results.