Numerical simulations are utilized to model the shock wave dynamics at the outlet of a single-transition section shock tube. Using the Euler algorithm, the evolution of the shock wave generated by TNT detonation within the pipe is calculated, and the simulation results are validated by comparison with established empirical formulas such as Henrch, Садовский, and Chinese defense design standards. The effects of explosive parameters, including the explosive mass, arrangement, and shape, on the pressure at both the explosion room and test room outlets are discussed. The dispersed arrangement forms a higher-pressure zone in the initial stage of the shock wave compared to the concentrated arrangement, but both have consistent peak pressure and overpressure duration. Explosive shape only significantly affects the shock wave before full development, with little impact on outlet pressure. The results show that, under the conditions of this study, the explosive mass has the most significant impact on the peak overpressure and positive pressure duration of the shock wave. These results can serve as a reference for the structural design of explosive-driven shock tubes.