Plastic limit analysis of a rotating solid or annular disc with variable thickness is presented in terms of a unified yield criterion (UYC). Stress distributions of the discs in plastic limit state corresponding to different yield curves are deduced. Upper and lower bounds of the plastic limit solutions are derived by selecting a weighting coefficient in the unified yield criterion. Stress redistribution is solved when the stress field violates yield criterion locally. Limit angular velocity as well as the stress distributions with respect to three special criteria, namely the Tresca criterion, the Mises criterion (close form solution) and the Yu criterion are illustrated and compared. The influences of yield criterion as well as the thickness on plastic limit solution of a rotating disc are demonstrated and discussed. (C) 2001 Elsevier Science Ltd. All rights reserved.