Background Despite declines in deaths from rheumatic heart disease (RHD) in Africa over the past 30 years, it remains a major cause of cardiovascular morbidity and mortality on the continent. We present an investment case for interventions to prevent and manage RHD in the African Union (AU).Methods We created a cohort state-transition model to estimate key outcomes in the disease process, including cases of pharyngitis from group A streptococcus, episodes of acute rheumatic fever (ARF), cases of RHD, heart failure, and deaths. With this model, we estimated the impact of scaling up interventions using estimates of effect sizes from published studies. We estimated the cost to scale up coverage of interventions and summarised the benefits by monetising health gains estimated in the model using a full income approach. Costs and benefits were compared using the benefit-cost ratio and the net benefits with discounted costs and benefits.Findings Operationally achievable levels of scale-up of interventions along the disease spectrum, including primary prevention, secondary prevention, platforms for management of heart failure, and heart valve surgery could avert 74 000 (UI 50 000-104 000) deaths from RHD and ARF from 2021 to 2030 in the AU, reaching a 30•7% (21•6-39•0) reduction in the age-standardised death rate from RHD in 2030, compared with no increase in coverage of interventions. The estimated benefit-cost ratio for plausible scale-up of secondary prevention and secondary and tertiary care interventions was 4•7 (2•9-6•3) with a net benefit of $2•8 billion (1•6-3•9; 2019 US$) through 2030. The estimated benefit-cost ratio for primary prevention scale-up was low to 2030 (0•2, <0•1-0•4), increasing with delayed benefits accrued to 2090. The benefit-cost dynamics of primary prevention were sensitive to the costs of different delivery approaches, uncertain epidemiological parameters regarding group A streptococcal pharyngitis and ARF, assumptions about long-term demographic and economic trends, and discounting.Interpretation Increased coverage of interventions to control and manage RHD could accelerate progress towards eradication in AU member states. Gaps in local epidemiological data and particular components of the disease process create uncertainty around the level of benefits. In the short term, costs of secondary prevention and secondary and tertiary care for RHD are lower than for primary prevention, and benefits accrue earlier.