The stress concentration of pipe structure or cavity defect has a great effect on the mechanical properties of the high-performance concrete (HPC) members in deep underground locations. However, the behaviour of HPC with cavities under triaxial compression is not understood, especially when pressurized liquid flows into the fractures from the cavity. This study aims to investigate the effect of the cavity and the confining pressure on the failure mechanisms, strengths, and deformation properties of HPC with a new experimental scheme. In this experiment, the pressurized liquid can only contact the surface of the sample in the cavity, while the other surfaces are isolated from the pressurized liquid. To further explore the effect of the cavity, the same experiments are also conducted on sealed and unsealed intact samples without a cavity. The failure modes and stress-strain curves of all types of the samples are presented. Under various confining pressures, all the samples with a cavity suffer shear failure, and there are always secondary tensile fractures initiating from the cavity sidewall. Additionally, it can be determined from the failure modes and the stress-strain curves that the shear fractures result from the sidewall failure. Based on the different effects of the cavity on the lateral deformations in different directions, the initiation of the sidewall fracture is well predicted. The experimental results show that both the increase of the confining pressure and the decrease of the cavity size are conducive to the initiation of sidewall fracture. Moreover, the cavity weakens the strength of the sample, and this study gives a modified Power-law criterion in which the cavity size is added as an impact factor to predict the strength of the sample.