Origami‐based metamaterials have widespread application prospects in various industries including aerospace, automotive, flexible electronics, and civil engineering structures. Among the wide range of origami patterns, the fourfold tessellation known as Miura‐ori is of particular attraction to engineers and designers. More specifically, researchers have proposed different 3D structures and metamaterials based on the geometric characteristics of this classic origami pattern. Herein, a computational modeling approach for the design and evaluation of 3D cellular solids with the Miura‐ori metamaterial geometry which can be of zero or nonzero thicknesses is presented. To this end, first, a range of design alternatives generated based on a numerical parametric model is designed. Next, their mechanical properties and failure behavior under quasistatic axial compressive loads along three perpendicular directions are analyzed. Then, the effects of various geometric parameters on their energy absorption behavior under compression in the most appropriate direction are investigated. The findings of this study provide a basis for future experimental investigations and the potential application of such cellular solids for energy‐absorbing purposes.