Background: COVID-19 elimination measures, including border closures have been applied in New Zealand. We have modelled the potential effect of vaccination programmes for opening borders. Methods: We used a deterministic age-stratified Susceptible, Exposed, Infectious, Recovered (SEIR) model. We minimised spread by varying the age-stratified vaccine allocation to find the minimum herd immunity requirements (the effective reproduction number Reff<1 with closed borders) under various vaccine effectiveness (VE) scenarios and R0 values. We ran two-year open-border simulations for two vaccine strategies: minimising Reff and targeting high-risk groups. Findings: Targeting of high-risk groups will result in lower hospitalisations and deaths in most scenarios. Reaching the herd immunity threshold (HIT) with a vaccine of 90% VE against disease and 80% VE against infection requires at least 86•5% total population uptake for R0=4•5 (with high vaccination coverage for 30-49-year-olds) and 98•1% uptake for R0=6. In a two-year open-border scenario with 10 overseas cases daily and 90% total population vaccine uptake (including 0-15 year olds) with the same vaccine, the strategy of targeting high-risk groups is close to achieving HIT, with an estimated 11,400 total hospitalisations (peak 324 active and 36 new daily cases in hospitals), and 1,030 total deaths. Interpretation: Targeting high-risk groups for vaccination will result in fewer hospitalisations and deaths with open borders compared to targeting reduced transmission. With a highly effective vaccine and a high total uptake, opening borders will result in increasing cases, hospitalisations, and deaths. Other public health and social measures will still be required as part of an effective pandemic response. Funding: This project was funded by the Health Research Council [20/1018]. Research in context.