Two possible dangers of an extensive varicella vaccination program are more varicella (chickenpox) cases in adults, when the complication rates are higher, and an increase in cases of zoster (shingles). Here an age-structured epidemiologic—demographic model with vaccination is developed for varicella and zoster. Parameters are estimated from epidemiological data. This mathematical and computer simulation model is used to evaluate the effects of varicella vaccination programs. Although the age distribution of varicella cases does shift in the simulations, this does not seem to be a danger because many of the adult cases occur after vaccine-induced immunity wanes, so they are mild varicella cases with fewer complications. In the simulations, zoster incidence increases in the first three decades after initiation of a vaccination program, because people who had varicella in childhood age without boosting, but then it decreases. Thus the simulations validate the second danger of more zoster cases.