Considerable evidence points to an accumulation of somatic mutations in older cells and organisms but the causal role of mutations in the ageing process is still unclear. In addition to demonstrating that mutations accumulate, it is important to address the question of whether they do so at a sufficient rate and with a dynamic profile that is consistent with them playing a causative role. We describe the development of in silico models that can be used to explore the role of somatic mutations in ageing and which form a part of a growing effort to build predictive mathematical and computer models that can help unravel the complexity of the functional genomics of ageing. Our models address, in particular, how mutations affect populations of dividing cells like human fibroblasts, in which the challenge to the somatic mutation theory is greatest, since selection at the cellular level will tend to suppress the accumulation of mutations.