Parametric resonance of polar orthotropic sandwich annular plates with a viscoelastic core layer subjected to a periodic uniform radial stress is studied by the finite element method. The axisymmetric discrete layer annular element and Hamilton's principle are employed to derive the finite element equations of motion for a sandwich plate including the transverse shear effect. The viscoelastic material in the core layer is assumed to be incompressible, and the extensional and shear moduli are described by complex quantities. The regions of dynamic instability are determined by Bolotin's method. The effects of various parameters on the dynamic instability regions are investigated.