Exploring performance by structural design and assembly strategies, mechanical metamaterials have recently attracted attention due to their prominent mechanical properties compared with traditional structures. Structural instability (e.g., buckling) has been deployed to form architected structures for multifunctional applications. Here, we report novel types of hierarchical metastructures composed of postbuckled elements, which have programmable mechanical characteristics under tension and compression. Simply tuning the geometries of the postbuckling elements, the presented metastructures have promising mechanical response (i.e., programmable tensile and compressive stiffnesses, zero Poisson's ratio, and recovery from large deformation). The reported hierarchical metastructures were fabricated and assembled using a 3D printing technique. Experiments were conducted and the results were validated with the analytical and numerical models with satisfactory agreement. The programmability is investigated with respect to the geometries of the bi-constrained beams. In favor of the buckling-induced, elastic deformation of the bilaterally constrained elements, the reported metastructures can be deployed for multipurpose applications, such as energy dissipation through the repeatable deformation-recovery process or damage detection based on the variation of postbuckling mode configuration.