Modelling suggests hepatitis C virus (HCV) elimination is possible among men who have sex with men (MSM), with key screening groups including HIV-diagnosed MSM and MSM using pre-exposure prophylaxis (PrEP). Mathematical modelling was used to determine the cost-effectiveness of HCV case-finding strategies among MSM from the provider perspective, and to determine which interventions could achieve a 90% reduction in HCV incidence over 2015-2030. At baseline, we assumed symptomatic screening in HIV-negative MSM (including PrEP users) and 12-monthly screening among HIV-diagnosed MSM. Improved case-finding strategies included screening alongside HIV testing in HIV-negative MSM not using PrEP (PrEP non-users); 12/6/3-monthly screening in PrEP users; and 6-monthly screening in HIV-diagnosed MSM, with the cost-effectiveness being compared incrementally. Costs (GBP) and quality-adjusted life years (QALYs) were assessed to estimate the mean incremental cost-effectiveness ratio (ICER) with a time horizon to 2050, compared to a willingness-to-pay threshold of £20,000/QALY. From the baseline, the most incrementally cost-effective strategy is to firstly undertake: (1) 12-monthly HCV screening of PrEP users (gaining 6715 QALYs with ICER £1760/QALY), followed by (2) HCV screening among PrEP non-users alongside HIV testing (gaining 7048 QALYs with ICER £4972/QALY). Compared to the baseline, this combined strategy would cost £46.9 (95%CrI £25.3-£66.9) million and achieve the HCV elimination target in 100% of model runs. Additional screening incurs ICERs >£20,000/QALY compared to this combined strategy. In conclusion, HCV elimination can be achieved cost-effectively among UK MSM. Policymakers should consider scaling-up HCV screening in HIV-negative MSM, especially PrEP users, for achieving this target.