IMPORTANCE: An effective vaccine against SARS-CoV-2 will reduce morbidity and mortality and allow substantial relaxation of physical distancing policies. However, the ability of a vaccine to prevent infection or disease depends critically on protecting older individuals, who are at highest risk of severe disease. OBJECTIVE: We quantitatively estimated the relative benefits of COVID-19 vaccines, in terms of preventing infection and death, with a particular focus on effectiveness in elderly people. DESIGN: We applied compartmental mathematical modelling to determine the relative effects of vaccines that block infection and onward transmission, and those that prevent severe disease. We assumed that vaccines showing high efficacy in adults would be deployed, and examined the effects of lower vaccine efficacy among the elderly population. SETTING AND PARTICIPANTS: Our mathematical model was calibrated to simulate the course of an epidemic among the entire population of British Columbia, Canada. Within our model, the population was structured by age and levels of contact. MAIN OUTCOME(S) AND MEASURE(S): We assessed the effectiveness of possible vaccines in terms of the predicted number of infections within the entire population, and deaths among people aged 65 years and over. RESULTS: In order to reduce the overall rate of infections in the population, high rates of deployment to all age groups will be critical. However, to substantially reduce mortality among people aged 65 years and over, a vaccine must directly protect a high proportion of people in that group. CONCLUSIONS AND RELEVANCE: Effective vaccines deployed to a large fraction of the population are projected to substantially reduce infection in an otherwise susceptible population. However, even if transmission were blocked highly effectively by vaccination of children and younger adults, overall mortality would not be substantially reduced unless the vaccine is also directly protective in elderly people. We strongly recommend: (i) the inclusion of people aged 65 years and over in future trials of COVID-19 vaccine candidates; (ii) careful monitoring of vaccine efficacy in older age groups following vaccination.