Brake squeal is an annoyance noise caused during brake operation. In brake operation, three types of noise depending on the frequency range may occurred. When the frequency of noise is less than hundred Hertz, it is named brake judder, while for frequency less than thousand is named brake groan. It is called Brake squeal when the frequency is less than twenty thousand. The focus of this work is on the brake squeal.This noise is irritating to both vehicle passenger and passerby. This problem has become principal issue for automotive industrials increasingly in recent years. Decreasing this noise causes increasing of vehicle quietness, passenger comfort and quality of automobile and decreasing of warranty cost. It is noticeable that only automobile industries in North America spent one billion US$ a year to recognize and decrease the squeal. The reason and source of generating brake squeal is not understood exactly because the mechanism of generating this noise is so complicated. Scientists that working in the field brake squeal accept that instability due to the friction force, leading to self excited vibration cause brake squeal. Engineers and scientists commonly suggest three possible reasons for the onset of instability, namely, the change of the friction coefficient with change of relative speed between pad and disk, change of the relative orientation of the disc and the friction pads leading to a modification of the friction force, and two modes, which are close to each other in the frequency range and have similar characteristics, may merge as the friction contribution increases. All of the theories were studied in this thesis. For the first two of these theories Matlab Software was utilized and some methods were suggested for decreasing the brake squeal noise. For decreasing the affect of twist theory, at first linear control was utilized to decreasing out of plane vibration of disc and a nonlinear system was introduced for the brake squeal and nonlinear control, computed torque method, applied to four degree of freedom system of brake squeal for suppression of out of plane vibration. The third theory was studied with Abaqus Software. A finite element model of the Samand brake system was constructed in software and then solved in several steps. Finally, the behavior of the model was analyzed with respect to the variation of important parameters such as coefficient of friction, brake force, stiffness of the brake system and its material characteristics. The effect of slots on the pads was also investigated. Key Words: Brake squeal, Dither, Friction-induced vibration, Sliding Mode, Computer torque method, Finite element, Matlab, Abaqus.