Abstract A sandwich annular plate built with two constrained layers of polar orthotropic material and a viscoelastic core layer is subjected to a periodic uniform radial stress while rotating. The axisymmetric dynamic instability of such a rotating sandwich plate is analyzed using finite elements. By employing a discrete layer axisymmetric annular element and Hamilton’s principle, the finite element equations of motion that facilitate considerations of transverse shear effect shear effect are derived. The viscoelastic material in the core layer is assumed to be incompressible, and its extensional and shear moduli are described by complex quantities. The regions of dynamic instability are determined by Bolotin’s method. Numerical results show that the constrained viscoelastic core layer tends to stabilize the sandwich annular plate system. In addition, the widths of instability regions decrease as the rotation speed increases.