A variational formulation of a beam model is presented for predicting the inelastic and geometrically nonlinear mechanical behavior of cellular and truss‐based architected materials. Emphasis is placed on the constitutive description of base materials commonly used in additive manufacturing, including polymers and metals, and the derivation of effective incremental potentials incorporating the effects of damage and viscoplasticity. The model is demonstrated in a variety of problems including the fracture of polymeric honeycombs, the tightening of woven architected materials, as well as the compression of metallic foams. The model's easy calibration–on the basis of single‐strut tests–and its successful validation—through experiments of additively manufactured specimens–indicate its promise as an efficient design tool for architected materials within a wide range of engineering applications.