We developed a novel perfusion bioreactor that is capable of cultivating multiple 3-dimensional (3D) cellular constructs in one flow chamber with a total cross-section area of 20 cm2. Two unique features integrated into the bioreactor provided a homogenous fluid flow along the bioreactor cross-section and maximal exposure of the cellular constructs to the perfusing medium. Mathematical modeling of the fluid flow regime in the perfusion bioreactor showed that integrating a flow-distributing mesh 1.5 cm upstream from the construct compartment imposed an equal medium flow and shear stress of 0.6 dynes/cm2 along the entire cell construct cross-section area. The design of 95.8% open-pore-area fixing nets enabled the exposure of 99.88% of the cell construct volume to the perfusing medium. Cardiac cell constructs seeded with physiologically relevant cell density (0.7 × 108 cells/cm3) in alginate scaffolds developed into homogenous compacted cardiac tissue, as judged using cell staining with fluorescein diacetate and hematoxylin-eosin histology. The cell constructs maintained 80% viability for nearly 2 weeks, whereas in static-cultivated cell constructs, only 50% of the initial cells remained, as determined according to total DNA content and MTT viability assay. Medium perfusion resulted in better cell viability, presumably due to the convective-diffusive transport of oxygen, compared with oxygen diffusion within the static-cultivated cell constructs, as well as due to efficient removal of harmful cell secretions. It is envisioned that this bioreactor would be useful for 3D cultivation of different mammalian cells for purposes of tissue engineering or production of valuable biologicals.