The work aims tostudy the cushioning performance of regular polygonal (equilateral triangular, square, regular hexagonal and regular octagonal) honeycombs with the elastic linear strain-hardening (bilinear) isotropic base material under out-of-plane impact through the finite element method. Finite element models based on the regular polygonal honeycomb cells were established for their out-of-plane impact analysis. Based on the proposed new evaluation indicator of most appropriate strain, all cushioning performance evaluation indicators were redefined to form a novel cushioning performance evaluation method. Their deformation modes, stress strain curves, and some cushioning performance evaluation indicators such as mean plateau stress, specific energy absorption and impact force efficiency of regular polygonal honeycombs with different relative densities under different impact velocities were obtained and analyzed. The regular octagonal honeycomb has the maximum mean plateau stress for a given relative density. The specific energy absorption of each regular polygonal honeycomb relies on the impact velocity in a quadratic polynomial curve. The regular hexagonal and octagonal honeycombs with same relative densities outperform equilateral triangular and square honeycombs in impact force efficiency.