In order to obtain a good honeycomb sandwich structure automatic placement quality, based on the automated fiber placement a numerical method for buckling, post-buckling and failure of Nomex honeycomb cores under compression load are established. The linear buckling method (eigenvalue method) is used to analyze buckling of honeycomb cell and the first-order buckling mode, the buckling eigenvalue and load are obtained. The initial geometrical defects are introduced, and non-linear buckling method (arc length method) is used to analyze the post-buckling behavior of Nomex honeycomb cell. According to the load-displacement curve of RP-1, the buckling load and the limit load of the arc length method are obtained. Contrasting the data of the finite element bucking analysis and experiment, some conclusions can be obtained: The eigenvalue method is more accurate than the arc length method in buckling analysis, but the arc length method can simulate post-buckling behavior better. The calculated results are basically consistent with the experimental data. A reference is provided for selecting the placement pressure in the process of automatic placement of Nomex honeycomb sandwich structure.