Cancer development is presumed to be an evolutionary process that is influenced by genetic background and environment. In laboratory animals, genetics and environment are variables that can largely be held constant. In humans, it is possible to compare independent tumours that have developed in the same patient, effectively constraining genetic and environmental variation and leaving only stochastic processes. Patients affected with von Hippel-Lindau disease are at risk of developing multiple independent clear cell renal carcinomas. Here we perform whole-genome sequencing on 40 tumours from six von Hippel-Lindau patients. We confirm that the tumours are clonally independent, having distinct somatic single-nucleotide variants. Although tumours from the same patient show many differences, within-patient patterns are discernible. Single-nucleotide substitution type rates are significantly different between patients and show biases in trinucleotide mutation context. We also observe biases in chromosome copy number aberrations. These results show that genetic background and/or environment can influence the types of mutations that occur.