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The quasi-static crush behavior of aluminum 5052-H38 honeycomb specimens under non-proportional compression dominant combined loads is investigated by experiments. Compression dominant combined loads and pure compressive loads were applied in different sequences to induce non-proportional combined loads. The experimental results show that the normal crush and shear strengths in combined loading regions and the normal crush strengths in pure compressive loading regions of the non-proportional combined loads are quite consistent with the existing phenomenological yield criterion based on the experimental normal crush and shear strengths under proportional combined loads. The experimental results indicate that the sequence of loading paths for the non-proportional combined loads does not affect the crush strengths of honeycomb specimens.