There is a need for preclinical testing systems that predict the efficacy, safety and pharmacokinetics of cancer therapies better than existing in vitro and in vivo animal models. An approach to the development of predictive in vitro systems is to more closely recapitulate the cellular and spatial complexity of human cancers. One limitation of using current in vitro systems to model cancers is the lack of an appropriately large volume to accommodate the development of this complexity over time. To address this limitation, we have designed and constructed a novel flow–perfusion bioreactor system that can support large-volume, engineered tissue comprised of multicellular cancer surrogates by modifying current microfluidic devices. Key features of this technology are a three-dimensional (3D) volume (1.2 cm3) that has greater tissue thickness than is utilized in existing microfluidic systems and the ability to perfuse the volume, enabling the development of realistic tumour geometry. The constructs were fabricated by infiltrating porous carbon foams with an extracellular matrix (ECM) hydrogel and engineering through-microchannels. The carbon foam structurally supported the hydrogel and microchannel patency for up to 161 h. The ECM hydrogel was shown to adhere to the carbon foam and polydimethylsiloxane flow chamber, which housed the hydrogel–foam construct, when surfaces were coated with glutaraldehyde (carbon foam) and nitric acid (polydimethylsiloxane). Additionally, the viability of breast cancer cells and fibroblasts was higher in the presence of perfused microchannels in comparison to similar preparations without microchannels or perfusion. Therefore, the flow–perfusion bioreactor system supports cell viability in volume and stromal contexts that are physiologically-relevant. Copyright © 2015 John Wiley & Sons, Ltd.