Analyzing the dynamic response of a wet multi-disc clutch is crucial for relevant fault diagnosis research. However, characterizing the tilting-impact phenomenon between the friction discs remains ambiguous. This paper presents a tilting-impact model of a multi-disc system under dry conditions and investigates the effect of disc deformation on the system dynamics. Firstly, Euler angles and Euler kinematic differential equations are introduced to describe the spatial position and orientation of the spinning-tilting disc. The aligning centrifugal moment, spline friction force, and tilting-impact forces for both flat and deformed discs are derived. A bench test is conducted to validate the model by comparing simulation and experimental signals at various rotation speeds. The results indicate that the occurrence of tilting-impact phenomena in dry conditions requires external disturbances, and the discs eventually stop tilting-impacting once the disturbance subsides, and the system with deformed discs experiences longer recovery times. Furthermore, the tilting-impact forces in systems with deformed discs are smaller than those with flat discs only.