Objective: Hepatitis C virus (HCV) infection is a major cause of liver disease. Since symptoms of chronic liver disease usually appear only late in the course of the disease, infected individuals may remain undiagnosed until advanced disease has developed. We aimed to investigate which screening strategies would be most effective to detect individuals unaware of their infection. Methods: We developed a mathematical model for HCV disease progression and compared the current practice of HCV testing in Switzerland with the following screening strategies: intensive screening of active injection drug users (IDU), screening of former IDU, screening of individuals originating from countries with high HCV prevalence, screening of individuals born 1951-1985 (birth-cohort) and universal screening. All screening interventions were considered in addition to a baseline scenario that reflected the current practice of HCV testing. Results: Within the first 4 years (2018-2021), every year, on average 650 cases were diagnosed in the baseline scenario, 660 with intensified IDU screening, 760 with former IDU screening, 830 with origin-based screening, 1420 with birth-cohort screening and 1940 with universal screening. No difference in liver-related mortality and incidence of end-stage liver disease between the screening scenarios was observed. Conclusion: Our results suggest that only large-scale screening of the general population could substantially accelerate the rate of HCV diagnosis and treatment in Switzerland and other countries with similar epidemics. However, this implies screening of a large population with low prevalence, and may trigger considerable numbers of false-positive and borderline test results.