This paper describes the thermoelastic instability arising from friction heat generation in braking and proposes the finite element methods to predict the variation of temperature and thermal deformation. In a conventional disc brake analysis, heat generation is only related with wheel speed and friction material and the interface pressure between disc and pad is assumed constant. But under dynamic braking conditions, the frictional heat causes the thermoelastic distortion that leads to more concentrated contact pressure distribution and hence more and more non-uniform temperature. In this paper, to complete the solution of the thermomechanically coupled problem, the linear relation model between pressure and temperature is proposed and demonstrated in examples of a simple two dimensional contact problem. And the two dimensional model has been extended to an annular three dimensional disc model in order to consider more realistic geometry and to provide a more accurate critical speed for automotive brake systems.