Background - The burden of human papillomavirus (HPV) infection can be substantially reduced through vaccination of girls, and gender-neutral policies are being adopted in many countries to accelerate disease control among women and expand direct benefits to men. Clinical direct benefit of boys HPV vaccination has been established for ano-genital warts and anal cancer. HPV vaccines are considered safe, but an association with Guillain-Barre syndrome has been found in French reimbursement and hospital discharge data. Methods - We conducted a Monte-Carlo simulation assuming a stable French population of 11- to 14-year-old boys, adult men and men having sex with men. We modelled and quantified the mid-term benefits as the annually prevented ano-genital warts among the 8.72 M men aged 15–35 years and the long-term benefits as the annually prevented anal cancer cases among the 17.4 M men aged 25–65 years. We also estimated the number of Guillain-Barre syndrome cases hypothetically induced by vaccination. Results - With a vaccine coverage of 30%, an annual number of 9310 (95% uncertainty interval [7050–11,200]) first ano-genital warts episodes among the 8.72 M men aged 15–35 years are prevented. According to more or less optimistic hypotheses on the proportion of HPV cancers covered by the vaccine, between 15.1 [11.7–17.7] and 19.2 [15.0–22.6] cases of anal cancer among the 17.4 M men aged 25–65 years would be annually avoided. Among men having sex with men, the corresponding figures were 1907 (1944–2291) for ano-genital warts and between 2.0 [0.23–4.5] and 2.6 [0.29–5.7] for anal cancer. Among 11- to 14-year-old boys, 0.82 (0.15–2.3) Guillain-Barre syndrome cases would be induced annually. Interpretation - A long-term program of HPV vaccination among boys in France would avoid substantially more cancer cases than hypothetically induce Guillain-Barre syndrome cases, in the general and specifically the homosexual population. Additional benefits may arise with the possible vaccine protection against oro-laryngeal and –pharyngeal cancer.