Fundamental investigations of human biology, and the development of therapeutics, commonly rely on 2D cell-culture systems that do not accurately recapitulate the structure, function, or physiology of living tissues. Systems for 3D cultures exist but do not replicate the spatial distributions of oxygen, metabolites, and signaling molecules found in tissues. Microfabrication can create architecturally complex scaffolds for 3D cell cultures that circumvent some of these limitations; unfortunately, these approaches require instrumentation not commonly available in biology laboratories. Here we report that stacking and destacking layers of paper impregnated with suspensions of cells in extracellular matrix hydrogel makes it possible to control oxygen and nutrient gradients in 3D and to analyze molecular and genetic responses. Stacking assembles the "tissue", whereas destacking disassembles it, and allows its analysis. Breast cancer cells cultured within stacks of layered paper recapitulate behaviors observed both in 3D tumor spheroids in vitro and in tumors in vivo: Proliferating cells in the stacks localize in an outer layer a few hundreds of microns thick, and growth-arrested, apoptotic, and necrotic cells concentrate in the hypoxic core where hypoxia-sensitive genes are overexpressed. Altering gas permeability at the ends of stacks controlled the gradient in the concentration of the O2 and was sufficient by itself to determine the distribution of viable cells in 3D. Cell cultures in stacked, paper-supported gels offer a uniquely flexible approach to study cell responses to 3D molecular gradients and to mimic tissue- and organ-level functions.