Abstract Background Many breast, cervical, and colorectal cancer screening programmes were disrupted due to the COVID-19 pandemic. This study aimed to estimate the effects of five restart strategies after the disruption on required screening capacity and cancer burden. Methods Microsimulation models simulated five restart strategies for breast, cervical, and colorectal cancer screening. The models estimated required screening capacity, cancer incidence, and cancer-specific mortality after a disruption of 6 months. The restart strategies varied in whether screens were caught up or not and, if so, immediately or delayed, and whether the upper age limit was increased. Results The disruption in screening programmes without catch-up of missed screens led to an increase of 2.0, 0.3, and 2.5 cancer deaths per 100 000 individuals in 10 years in breast, cervical, and colorectal cancer, respectively. Immediately catching-up missed screens minimised the impact of the disruption but required a surge in screening capacity. Delaying screening, but still offering all screening rounds gave the best balance between required capacity, incidence, and mortality. Conclusions Strategies with the smallest loss in health effects were also the most burdensome for the screening organisations. Which strategy is preferred depends on the organisation and available capacity in a country.