Polycystic kidney disease (PKD) is a life-threatening disorder, commonly caused by defects in polycystin-1 (PC1) or polycystin-2 (PC2), in which tubular epithelia form fluid-filled cysts. A major barrier to understanding PKD is the absence of human cellular models that accurately and efficiently recapitulate cystogenesis. Previously, we have generated a genetic model of PKD using human pluripotent stem cells and derived kidney organoids. Here we show that systematic substitution of physical components can dramatically increase or decrease cyst formation, unveiling a critical role for microenvironment in PKD. Removal of adherent cues increases cystogenesis 10-fold, producing cysts phenotypically resembling PKD that expand massively to 1-centimetre diameters. Removal of stroma enables outgrowth of PKD cell lines, which exhibit defects in PC1 expression and collagen compaction. Cyclic adenosine monophosphate (cAMP), when added, induces cysts in both PKD organoids and controls. These biomaterials establish a highly efficient model of PKD cystogenesis that directly implicates the microenvironment at the earliest stages of the disease.