Malignancies of epithelial tissues, called carcinomas, account for the majority of cancer cases. Much cancer research has focused on genetic alterations and their relation to different carcinoma phenotypes. Besides a rewiring in the signalling networks, carcinoma progression is accompanied by mechanical changes in the epithelial cells and the extracellular matrix. Here, we reveal intricate morphologies in the basement membrane at the onset of bladder cancer, and propose that they emerge from a mechanical buckling instability upon epithelial overgrowth. Using a combination of microscopy imaging of the mouse and human bladder tissue, elasticity theory, and numerical simulations of differential growth in the bladder mucosa, we find that aberrant tissue morphologies can emerge through stiffness changes in the different mucosa layers. The resulting thickening, wrinkles and folds exhibit qualitative and quantitative similarity with imaged early papillary tumors and carcinomas in situ. Atomic force microscopy indeed reveals local stiffness changes in the pathological basement membrane. Our findings suggest a mechanical origin of the different carcinoma subtypes in the bladder, which have vastly different clinical prognosis. They might provide the basis for a new line of attack in medical carcinoma treatment and prophylaxis.