The propagation process of intense acoustic shock wave, generated by the discharge of underwater plasma sound source, is analyzed based on a modified Rayleigh model. The bunching sound field model of underwater plasma sound source is established by using the Euler equation as the control equations. The formation mechanism of the shock wave negative pressure is analyzed theoretically and intuitively through the sound field charts obtained by simulation. The results demonstrate that the water around the bunching wave will be stretched and form a zone of negative pressure with the combination of the rarefaction wave and the inertia of water. It will make the water form a discontinuous phenomenon if the stretching force is greater than the ultimate tensile strength of the water, the phenomenon of cavitation bubble will appear at this time. Besides that, negative pressure will be aggravated by the diffracted wave generated at the edge of the energy-gathered reflector, and the shock wave negative pressure will reach a maximum value by the superimposition of the edge diffraction wave and the stretch wave. The reasons for the formation of the shock wave negative pressure is testified and revealed further by comparing the waveforms of simulation and experiment. The study results provide a theoretical guide for understanding the propagation law of underwater shock wave and further improving the design of the underwater plasma sound source.