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A simple finite element model for the pads, caliper and mounting of a car disc brake system is built and its dynamic influence to the disc is established. The disc is modeled as a thin plate in sliding contact with the pads. Through the contact conditions, the dynamics of the whole disc brake system is formulated. The friction-induced instability of the disc brake system is analyzed for different system parameters and operating conditions so that their influences on the dynamic instability and squeal are understood. Numerical simulation indicates that in the specific cases considered reasonably stiff pads tend to reduce the likelihood of squeal.