Thermoelastic instability of multi-disc clutch contributes to the failure of power transmission and as such multi-disc clutch is considered as a research object with a theory model built on perturbation method. The characteristic equations on the thermoelastic instability of geometrically symmetrical and antisymmetrical steel-disc are derived. The results are shown that both wave number and disc thickness have significant influences on the thermoelastic instability of the steel-disc. Choosing a larger wave number or a thicker steel-disc can prevent the thermoelastatic instability state in multi-disc clutch. Compared with the geometrically symmetrical steel-disc，the geometrically antisymmetrical steel-disc is more susceptible to thermoelastic instability.