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Abstract Metamaterials are architected cellular networks with solid struts, plates, or shells that constitute the edges and faces of building cells. Certain metamaterial designs can balance light weight and high stiffness requirements, which are otherwise mutually exclusive in their bulk form. Existing studies on these materials typically focus on their mechanical response under uniaxial compression, but it is unclear whether a strut-based metastructure design with high compressive stiffness can exhibit high torsional stiffness simultaneously. Designing lightweight metastructures with both high compressive and torsional stiffnesses could save time and cost in future material development. To explore the effect of unit cell design, unit cell number, and density distribution on both compressive and torsional stiffnesses, a computational design space was presented. Seven different unit cells, including three basic building blocks: body-centered cubic (BCC), face-centered cubic (FCC), and simple cubic (SC) were analyzed. All samples had a relative density of approximately 7%. It was found that a high compressive stiffness required a high concentration of struts along the loading direction, while a high torsional stiffness needed diagonal struts distributed on the outer face. Increasing unit cell numbers from 1 to 64 affected stiffness by changing the stress distribution globally. Non-uniform metastructure designs with strengthened vertical and diagonal struts towards the outer surface exhibited higher stiffness under either compressive or torsional loading. This study provides valuable guidelines for designing and manufacturing metamaterials for complex mechanical environments.