This paper is devoted to assess the impact of quadrivalent human papillomavirus (HPV) vaccine on the prevalence of non-oncogenic HPV 6/11 types in French males and females. For this purpose, a non-linear dynamic model of heterosexual transmission for HPV 6/11 types infection is developed, which accounts for immunity due to vaccination, in particular. The vaccinated reproduction number Rv is derived using the approach described by Diekmann et al. (2010) called the next generation operator approach. The model proposed is analysed, with regard to existence and uniqueness of the solution, steady-state stability. Precisely, the stability of the model is investigated depending on the sign of Rv-1. Prevalence data are used to fit a numerical HPV model, so as to assess infection rates. Our approach suggests that 10 years after introducing vaccination, the prevalence of HPV 6/11 types in females will be halved and that in males will be reduced by one-quarter, assuming a sustained vaccine coverage of 30% among females. Using the formula, we derived for the vaccinated reproduction number, we show that the non-oncogenic HPV 6/11 types would be eradicated if vaccine coverage in females is kept above 12%.