Tissue engineering is one approach to address the donor-organ shortage, but to attain clinically significant viable cell densities in thick tissues, laboratory-constructed tissues must have an internal vascular supply. We have adopted a biomimetic approach and assembled microscale modular components, consisting of submillimeter-sized collagen gel rods seeded with endothelial cells (ECs) into a (micro)vascularized tissue; in some prototypes the gel contained HepG2 cells to illustrate the possibilities. The EC-covered modules then were assembled into a larger tube and perfused with medium or whole blood. The interstitial spaces among the modules formed interconnected channels that enabled this perfusion. Viable cell densities were high, within an order of magnitude of cell densities within tissues, and the percolating nature of the flow through the construct was evident in microcomputed tomography and Doppler ultrasound measurements. Most importantly, the ECs retained their nonthrombogenic phenotype and delayed clotting times and inhibited the loss of platelets associated with perfusion of whole blood through the construct. Unlike the conventional scaffold and cell-seeding paradigm of other tissue-engineering approaches, this modular construct has the potential to be scalable, uniform, and perfusable with whole blood, circumventing the limitations of other approaches.