Fused silica is an indispensable basic element in a laser system and the weakest link in all components. When the laser interacts with fused silica, the target absorbs the laser energy so that its own temperature rises, and then it melts and vaporizes. The vaporization of the target gasification further absorbs the laser energy and produces a low density ionization reaction, resulting in the laser supported combustion wave (LSCW) phenomenon. In this paper, taking into account the effects of temperature residual, change in target morphology, distribution of splash material, and distribution of target surface airflow condition, we model and simulate the process of LSCW in stages. The laser energy transfer process, including the inverse bremsstrahlung radiation, thermal radiation, heat conduction and convection processes, is simulated by establishing a two-dimensional axisymmetric gas dynamic model. In addition, the LSCW in the visible light band has a strong radiation characteristic, which is significantly different from the laser induced target melting and vaporization phenomenon. The LSCW is easily received and displayed by high-speed camera. Therefore, a shadow system is established to measure the expanding velocity of the combustion wave in the process of fused silica damaged by laser, and the evolution process image of the combustion wave is obtained. The results show that under the action of parallel laser beam, the propagation of the combustion wave is in a steady-state and the gas dynamic behavior is stable. For the pulse widths of 1 ms and 3 ms, the average propagation velocity of the LSCW is calculated to be about 24 m/s, which is consistent with the experimental result in the literature available. This verifies the correctness of our theoretical model. For the pulse width of 3 ms, the average velocity of the flow field near the wavefront is calculated to be about 200 m/s. The numerical relationship between the velocity of the flow field and the propagation velocity of the LSCW is also basically consistent with the theoretical derivation result. Under the action of focused laser beam, the propagation of the combustion wave is unsteady. For the pulse widths of 1 ms, the laser intensity at the front of the plasma decreases gradually and the beam radius becomes larger. For the pulse width of 1.8 ms, both a similar pattern of mushroom cloud in the combustion wave and turbulence are observed, which is basically consistent with the evolution process of the combustion wave appearing in our experiment. The simulation results are in good accordance with the experimental results, and also provide a theoretical and experimental basis for studying the LSCW of fused silica.