Three-dimensional finite element models of edge closed honeycomb sandwich panels involving non-damage and face-core debonding damage are established by using finite element software ABAQUS. Three different models are employed to study the buckling loads and instability modes of the edge closed honeycomb panels under compressive loads. According to sandwich theory, the honeycomb core is equivalent to an orthotropic structure. The cohesive elements are used to simulate the interface between face are core. The results indicate that with the increase of debonding sizes, the buckling load of the honeycomb sandwich panel decreases gradually. When 30 mm ≤ D ≤ 80 mm, the instability modes transform from mixed buckling to local buckling. As the local buckling occurs, the law of buckling load, buckling load values and buckling modes in the two equivalent models become approximatively close to the original model.