Buckling behavior of sandwich panels with a compressible core which are debonded at one of their face sheet-core interfaces is presented. The buckling analysis is based on the principles of the High-Order Sandwich Panel Theory (HSAPT). The effect of the delamination length and location on the critical loads and the buckling modes is studied numerically. Edge delamination as well as inner delamination results are presented. The effect of contact on the critical loads and the buckling modes is presented. A comparison with experimental buckling modes is discussed and conclusions are drawn.