We present a back-calculation analysis of the variant Creutzfeldt-Jakob (vCJD) epidemic in the UK to estimate the number of infected individuals and to explore the likely future incidence of the disease. The main features of the model are that the hazard of infection was assumed proportional to the incidence of BSE in the UK with allowance for precautionary control measures taken in 1988 and in 1996, and that the incubation period distribution of vCJD follows an offset generalized F distribution. Our results indicate that current the numbers of cases with onset up to 31 December 2000 data are broadly compatible with numbers of primary infections ranging from a few hundred to several million. However, if a very large number of persons were infected, the model suggests that the mean incubation period is likely to be well beyond the human lifespan, resulting in a disease epidemic of much smaller size (maximum several thousand). A sensitivity analysis indicates that our results are sensitive to the underreporting of vCJD cases before 1996. Finally, we show that, in the absence of a reliable test for asymptomatic infection, uncertainty in estimates of the total number of infections is likely to remain for at least several years, even if the number of clinical cases remains low.