This paper examines the squeal propensity associated with the rigid motion of a brake pad. For the description of the rigid motion, the brake pad is analytically modeled as a composite annular sector plate with both the back plate and friction material rigid. The friction material is subject to friction contact with a rotating disc. The vibration modes of the rigid pad consist of the six rigid modes including three rotation and three translation modes coupled with contact stiffness. The analytical formulation for the dynamic motion of the composite rigid pad is presented. From the numerical calculation, the rigid pad modes are shown to be coupled with one another and thus generate the modal instability in both finite element full model and simplified pad model. It is suggested that the squeal propensity of the rigid pad modes can be estimated by using the simplified pad model and controlled by the certain design modification such as the contact area.