To study the initiation process under jet impact and obtain the critical initiation threshold of explosives with different thicknesses， experiments of jet formation with Φ40 mm shaped charge were performed and captured by the high-speed video. The 43-mm thick TNT explosives were covered by 50SiMnVB cover plates with different thicknesses in experiments. The critical initiation threshold， the response under different stimulus intensities and the expansion velocity of reaction products were obtained. The numerical simulation of finite-thickness explosive under jet impact was carried out by using numerical simulation software. The propagation process of bow wave in explosive under jet impact and the relationship between critical initiation threshold and the thickness of finite-thickness explosive were analysed. The simulation results were compared and verified by the experimental data. The results show that the critical initiation threshold of TNT with a thickness of 43 mm is 37 mm³·μs^-2， and the expansion rate of reaction products varies by at least one order of magnitude between different responses. When the jet impacts on a finite-thickness explosive， a certain distance is required for a bow shock wave evolving into a detonation wave. The higher the tip velocity of the residual jet is， the shorter the distance is required for the evolution of bow shock wave to detonation wave. Therefore， the decrease of explosive thickness will lead to the increase of critical initiation threshold of finite-thickness explosive， and the logarithm of critical initiation threshold is approximately linear with the logarithm of explosive thickness.