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The characterization of additively manufactured cellular materials, such as honeycombs and lattices, is crucial to enabling their implementation in functional parts. One of the characterization methods commonly employed is mechanical testing under compression. This work focuses specifically on the dependence of these tests to the applied strain rate during the test over low strain rate regimes (considered here as 10−6 to 10−1 s−1). The paper is limited to the study of strain the rate dependence of hexagonal honeycomb structures manufactured with four different additive manufacturing processes: one polymer (fused deposition modeling, or material extrusion with ABS), one composite (nylon and continuous carbon fiber extrusion) and two metallic (laser powder bed fusion of Inconel 718 and electron beam melting of Ti6Al4V). The strain rate sensitivities of the effective elastic moduli, and the peak loads for all four processes were compared. Results show significant sensitivity to strain rate in the polymer and composite process for both these metrics, and mild sensitivity for the metallic honeycombs for the peak load. This study has implications for the characterization and modeling of all mechanical cellular materials and makes the case for evaluation and if appropriate, inclusion, of strain rate effects in all cellular material modeling.