Cavitation will increase the leakage and discharge pressure fluctuation of axial piston pumps. In particular, specific cavitation damage may aggravate the pressure impact and performance degradation. The influence of the specific cavitation damage on the discharge pressure is unclear, and the need for fault detection of this damage is urgent. In this paper, we propose a discharge pressure-based model and fault detection methodology for the specific cavitation damage of axial piston pumps. The discharge pressure model with specific damage is constructed using a slender hole. The simulation model is solved through numerical integration. Experimental investigation of cavitation damage detection is carried out. Discharge pressure features in the time domain and frequency domain are compared. The results show that waveform distortions, spectrum energy relocation, generation of new frequencies and sidebands can be used as features for fault detection regarding the specific cavitation damage of axial piston pumps.