Electro-hydraulic pulse plasma is considered to be a new and efficient rock breaking technology. However, there is currently a lack of research on its rock breaking effect under the bottom-hole conditions in oil and gas well drilling. In this study, the rock breaking effect of electro-hydraulic pulse plasma under different confining and axial pressures was studied by experiments and stress wave modelling. A calculation model for the distribution of stress waves inside rocks under electro-hydraulic pulse plasma was established, and the distribution characteristics of stress wave peaks in granite rock samples were analyzed for the verification of the model. Coupling with the experimental testing of the ultrasonic parameters with granite, shale, and sandstone rock samples under different confining and axial pressures, the influence of confining and axial pressures on rock breaking effect by the electro-hydraulic pulse plasma was obtained. The results show that compressive, shear, and tensile stresses can occur simultaneously inside the rock sample under the impact of the electro-hydraulic pulse plasma shockwave, and the influence of axial pressure on rock breaking is greater than that of the confining pressure. When the confining pressure and axial pressure increase, the peak stress wave inside the rock also increases, indicating that the electro-hydraulic pulse plasma can also have good effects on rock breaking under real downhole drilling conditions.