Cell lines are the mainstay in understanding the biology of COVID-19 infection, but do not recapitulate many of the complexities of human infection. The use of human lung tissue is one solution for the study of such novel respiratory pathogens. We hypothesized that a cryopreserved bank of human lung tissue allows for the in vitro study of the inter-individual heterogeneity of host response to SARS-CoV-2 infection, thus providing a bridge between studies with cell lines and studies in animal models. We generated a cryobank of tissues from 16 donors, most of whom had risk factors for severe illness from COVID-19. Cryopreserved tissues preserved 90% of cell viability and contained heterogeneous populations of metabolically active epithelial, endothelial, and immune cell subsets of the human lung. Samples were readily infectible with HCoV-OC43 and SARS-CoV-2 coronavirus strains, and demonstrated comparable susceptibility to infection. In contrast, we observed a marked donor-dependent heterogeneity in the expression of IL-6, CXCL8 and IFNβ in response to SARS-CoV-2 infection. Treatment of tissues with dexamethasone and the experimental drug, N-hydroxycytidine, suppressed viral growth in all samples, whereas chloroquine and remdesivir had no detectable effect. Metformin and sirolimus, molecules with predicted antiviral activity, suppressed viral replication in tissues from a subset of donors. In summary, we developed a novel system for the in vitro study of human SARS-CoV-2 infection using primary human lung tissue from a library of donor tissues. This model may be useful for drug screening and for understanding basic mechanisms of COVID-19 pathogenesis.