The accurate thermal stresses estimation of any machine element that is subjected to high temperature gradient is considered as essential matter for the mechanical engineers to obtain a successful design. Friction clutches are subjected periodically to high thermal stresses during the beginning of engagement due to the relative motion between driving and driven parts. Axisymmetric finite element models were developed in the present work to simulate the multi-disc clutches during the initial period of engagement to compute thermal stresses, heat generation, and temperature field. Axisymmetric models were used to simulate a multi-disc clutch works under the dry condition during the sliding period. The results indicate that the highest values of the thermal stresses appeared on the last friction disc (5th) and less effect on the other friction discs. This study presents a promising design tool to investigate the effect of materials, surface roughness, sliding speed and boundary conditions on the thermal stresses induced in the contacting surfaces of the friction clutches.