Manufacturing defects, which occur often in cellular cores of sandwich structures, lead to buckled cells in the core and thus to degraded constitutive core properties. Defects in the core cells may occur due to unintentional tool impacts onto the panel during manufacturing, handling processes, or defects in the manufactured core itself. The degraded constitutive properties of the core lead to local stiffness degradations of the sandwich panel, which in turn may impact the capability of nearby inserts; inserts are often used for component mounting to the panel or as joints used for joining the sandwich panel with another panel. The aim of this paper is to: a) Understand the effect of core density on the critical buckling load/buckling capability of the unit cell for each of the three core shapes: hexagonal, square and triangular, b) Understand the effect of core height (core thickness within the sandwich panel) on the critical buckling load/buckling capability of the unit cell for each of the three core shapes, and c) Investigate the degradation in the constitutive properties of the cellular core due to permanent deformation resulting from transverse compression. Detailed finite element models for five cell sizes and twenty one core densities were created for each of the following cellular core shapes: hexagonal, square and triangular. The critical buckling load is calculated for all twenty one core densities and the five cell sizes under consideration for the hexagonal, square and triangular cellular cores. Additionally, the critical buckling load is calculated for four core heights from 0.25" to 1.00" core height with 0.25" increments to study the effect of the core height on the critical buckling load of the unit cell. The degradation of constitutive properties of the hexagonal, square and triangular cellular cores due to buckling under transverse compression loading for the 1/8โณ cell size and core density of 3.1 pcf is studied for the 0.5โณ core height cells. All cellular cores are assumed to be manufactured of corrugated Al-5056.