The present study is concerned with the behavior of delaminated circular sandwich plates with a compressible “soft” core and composite laminated face sheets of general layup. The analysis follows the concepts of the High-Order Sandwich Plate Theory and employs the variational principle of virtual work for the derivation of the field equations of the fully bonded and delaminated regions. In the penny shaped disbonded region, the delaminated faces can slip horizontally with respect one to another, yet they may be in contact and resist vertical normal compressive stresses. The compressible core is considered using the 3D theory of elasticity and the lamination theory is employed for the modeling of the composite laminated face sheets. The formulation yields coordinate-dependent constitutive relations and governing equations and the solution procedure adopts the Galerkin method in the circumferential direction and the multiple-points shooting method in the radial direction. Numerical results regarding a typical delaminated sandwich plate are presented in terms of deformations and stresses. The results reveal the effect of the anisotropic laminated face sheets on the response of the structure and the influence of the delamination on the overall and, especially, the localized behavior of the plate.