Abstract: To address the abnormal pressure pulsation and excessive circumferential vibration observed in a certain type of aviation hydraulic piston pump under high-pressure conditions, a parameter-sensitivity-driven multi-scale vibration analysis method is proposed. A parameterized model incorporating the rotor, main shaft, swashplate, and plungers is established. This model achieves high accuracy, with a maximum average percentage deviation of 17.4% in circumferential vibration amplitude compared to experimental data. The study systematically reveals the influence laws of structural parameters on the response characteristics of the system under flow pulsation excitation. A finite element model of the pump casing is also developed, which includes critical connection structures such as mounting bolts, valve plate cover bolts, and slipper ball joints. The mutual interactions of internal components are simplified into equivalent excitations acting on the housing along the force transmission path. The simulated circumferential acceleration shows excellent agreement with experimental measurements, with a maximum deviation of only 0.5%. Further analysis investigates the influence of key structural parameters on circumferential vibration. Increasing the preload of the stator-side mounting bolts stabilizes the measured acceleration around 3.17g, while enhancing the stiffness of the valve plate cover bolts effectively suppresses resonance, reducing the acceleration to approximately 1.94g. In contrast, enlarging the slipper ball joint clearance on the rotor side causes minimal change in acceleration at low multiples (1× to 6×), but leads to instability beyond that threshold. By introducing a quantitative parameter sensitivity index, the study demonstrates that variations in stator-side connection parameters reduce vibration via equivalent stiffness modulation, whereas rotor-side kinematic joint parameters trigger instability through contact nonlinearity. This mechanism is identified as the primary cause of the casing’s vibration limit exceedance. This research, for the first time, integrates multi-scale parametric modeling with sensitivity analysis in the context of hydraulic pump dynamics. The proposed sensitivity-based evaluation method provides a theoretical foundation for structural optimization and fault diagnosis of high-performance hydraulic components.