Display omitted •Three additive manufacturing parameter sets and five cellular materials.•Process-geometry-property interactions of the additively manufactured structures.•The intermediate power and exposure time parameter set results in less porosity.•The choice of cellular architectures has a greater influence on strength and energy absorption. Additive Manufacturing (AM) has enabled the fabrication of metallic cellular materials that are of interest in the design of lightweight impact resistant structures. However, there is a need to understand the interactions between: (i) the material architecture, (ii) the AM process parameters, and (iii) the as-built geometry, microstructure and energy absorbing properties. In this work, we investigate the quasi-static and dynamic behaviour of cellular materials manufactured from 316L stainless steel using laser powder bed fusion (LPBF). Four cellular architectures are considered (octet lattice, lattice-walled square honeycomb, origami and square honeycomb), as well as three sets of AM process parameters, characterised by laser powers of 50, 125 and 200 W. The exposure time is adjusted to deliver the same total heat input. The 125 W case leads to material with the highest strength and ductility. The cellular materials with this process variant match their nominal densities most closely, and have the highest strength and energy absorption. Either reducing (50 W) or increasing (200 W) the power leads to a significant increase in porosity, reducing strength and energy absorption. However, we find that changes due to process-induced porosity have a smaller influence than those resulting from the choice of cellular architecture.