With improving biofabrication technology, 3D bioprinted constructs increasingly resemble real tissues. However, the fundamental principles describing how cell-generated forces within these constructs drive deformations, mechanical instabilities, and structural failures have not been established, even for basic biofabricated building blocks. Here we investigate mechanical behaviours of 3D printed microbeams made from living cells and extracellular matrix, bioprinting these simple structural elements into a 3D culture medium made from packed microgels, creating a mechanically controlled environment that allows the beams to evolve under cell-generated forces. By varying the properties of the beams and the surrounding microgel medium, we explore the mechanical behaviours exhibited by these structures. We observe buckling, axial contraction, failure, and total static stability, and we develop mechanical models of cell-ECM microbeam mechanics. We envision these models and their generalizations to other fundamental 3D shapes to facilitate the predictable design of biofabricated structures using simple building blocks in the future.