A process has been developed for the rapid tissue engineering of multicellular- tissue-equivalent assemblies by the controlled enzymatic degradation of polymeric beads in a low-fluid- shear bioreactor. In this process, the porous polymeric beads serve as temporary scaffolds to support the assemblies of cells in a tissuelike 3D configuration during the critical initial growth phases of attachment of anchorage-dependent cells, aggregation of the cells, and formation of a 3D extracellular matrix. Once the cells are assembled into a 3D array and enmeshed in a structural supportive 3D extracellular matrix (ECM), the polymeric scaffolds can be degraded in the low-fluid-shear environment of the NASA-designed bioreactor. The natural 3D tissuelike assembly, devoid of any artificial support structure, is maintained in the low-shear bioreactor environment by the newly formed natural cellular/ECM. The elimination of the artificial scaffold allows normal tissue structure and function.