The development of high-risk human papillomavirus (hrHPV) infection to cervical cancer is a complicated process. We considered solely hrHPV infections, thus avoiding the confounding effects of disease progression, screening, and treatments. To analyse hrHPV epidemiology and to estimate the overall impact of vaccination against infections with hrHPVs, we developed a dynamic compartmental transmission model for single and multiple infections with 14 hrHPV types. The infection-related parameters were estimated using population-based sexual behaviour and hrHPV prevalence data from Finland. The analysis disclosed the important role of persistent infections in hrHPV epidemiology, provided further evidence for a significant natural immunity, and demonstrated the dependence of transmission probability estimates on the model structure. The model predicted that vaccinating girls at 80% coverage will result in a 55% reduction in the overall hrHPV prevalence and a higher 65% reduction in the prevalence of persistent hrHPV infections in females. In males, the reduction will be 42% in the hrHPV prevalence solely by the herd effect from the 80% coverage in girls. If such high coverage among girls is not reached, it is still possible to reduce the female hrHPV prevalence indirectly by the herd effect if also boys are included in the vaccination program. On the other hand, any herd effects in older unvaccinated cohorts were minor. Limiting the epidemiological model to infection yielded improved understanding of the hrHPV epidemiology and of mechanisms with which vaccination impacts on hrHPV infections.