Many basic studies were conducted to discover the main reason for squeal occurrence in both disc and drum brake systems. As, it is well-known that the squealed brake system is more effective than the non-squealed brake system and it is also a common discomfort. So, cancellation of the squeal is not preferable, however, elimination of the brake squeal is a favorable.An approach to study the drum brake squeal is presented based mainly on the Finite Element Method (FEM) representation. The brake system model is based also on the model information extracted from finite element models for individual brake components. This finite element method (FEM) was used to predict the mode shape and natural frequency of the brake system after appropriate verification of FEM. The results showed that increasing the young's modulus of the brake drum and lining play an important role in the occurrence of the squeal, however, decreasing the lining coefficient of friction lead to decreasing the occurrence of the squeal. The component models for the drum and shoes were coupled together. The study shows that both the frequency separation between two systems modes due to static coupling and their associated mode shapes play an important role in mode merging.It was noted that squeals are most likely to occur when the eigenvectors and eigenvalues of the brake drum and brake shoes are close to the coupled vibration frequency. It was also noted that the eigenvectors of the leading and trailing brake shoes are independent from each other with the same natural frequency. The results showed that the coupling between different modes was necessary to form instabilities.