In this paper an efficient approach to simulate thermal stresses due to frictional heating of disc brakes is presented. Inthe approach thermal and stress analysis are performed sequentially. The frictional heat analysis is based on the Eulerianmethod, which requires significantly low computational time as compared to the Lagrangian approach. Completethree-dimensional geometries of a disc and a pad are considered for the numerical simulations. The contact forcesare computed at each time step taking the thermal deformations of the disc into account. The nodal temperaturehistory is recorded at each time step and is used in sequentially coupled stress analysis, where a temperature dependentelasto-plastic material model is used to compute the stresses in a disc brake. The results show that during hard braking,high compressive stresses are generated on the disc surface in circumferential direction which cause plastic yielding. Butwhen the disc cools down, the compressive stresses transform to tensile stresses. Such thermoplastic stress history maycause cracks on disc surface after a few braking cycles. These results are in agreement with experimental observationsavailable in the literature.