We have performed theoretical analysis of thermal expansion of carbon and boron nitrides under finite temperature based on first principles phonon state calculations. Volume dependence of phonon density of states and thermodynamic functions such as heat capacity and vibrational free energy were theoretically examined. Through the volume dependence of vibrational free energy, thermal expansion at finite temperature is reproduced within quasi-harmonic approximation (QHA). Our calculation results have demonstrated that thermal expansion coefficients of typical ceramics materials (diamond, graphite, c-BN and h-BN) are reasonably well reproduced with the first principles approach employing QHA calculations.