An energy method has been used for an elastic formulation of buckling analysis of a simply supported sandwich plate with crossply faces, including the interlayer shear deformation of adhesive layers and the transverse normal and shear deformations of the core. A quasi-elastic method is used for the solution of viscoelastic analysis of the sandwich plate. Results of the viscoelastic buckling analysis under in-plane loads are presented for various lay-up sequences of face plates. Dependence of buckling load on face lay-up sequence, adhesive bonding stiffness, load ratio, and plate geometry is examined, including the effect of change of buckling modes.