Materials with anisotropic mechanical properties play an important role in nature and technology. Thus, many biomechanical processes in living organisms, which govern their growth, muscular activity, and oxygen and nutrient supply, are based on an anisotropic response of cells to various mechanical stimuli. [1,2] In engineering practice, materials with controlled anisotropy are used in various sensitive structures. [3] Directional dependence of the propagation velocity of acoustic waves stemming from the elastic anisotropy of the medium makes it possible to produce various materials and devices for breaking acoustic waves or damping of vibrations. [4] These are but a few illustrations of the significance of mechanical anisotropy. Elastic anisotropy can be achieved in many ways. In composites, it is produced using a special arrangement of the constituents. [5] The paradigm of architectured materials, [6,7] also referred to in the literature as hybrid materials, or metamaterials, and for brevity called archimats in the following, opens remarkable new possibilities for creating anisotropic properties. It builds on the idea of Ashby that the inner architecture of a material can be regarded as an extra "degree of freedom" in materials design, which can be exploited to provide the material with desired properties. [8] Some architectured materials with artificially created mechanical anisotropy are already in existence; see the previous studies. [3,4,9,10] Among them, periodic beam lattice materials take a special place due to the variability of properties they possess. [6] The properties are determined by the architecture of the elementary cell of the lattice. Commonly, it is the lattice geometry that is varied to achieve targeted characteristics of the material, while