A finite strain investigation is presented for the axially-symmetric plane-stress problem of a rotating annular disc. Material behaviour is modelled by an elasto-plastic deformation type theory based on a new anisotropic flow theory proposed by Hill. It is shown that the governing field equations can be reduced to a system of two coupled linear differential equations. The solution of that system is obtained numerically using a standard procedure. The analysis is not restricted to any particular choice of the strain hardening characteristic, and covers the entire elasto-plastic domain. Detailed results are derived, as an example, for a disc made of soft aluminum. The existence of a critical (maximum) angular velocity is demonstrated over a wide range of radii ratio. © 1983 Springer Verlag.