COVID-19 population vaccination programs are underway globally. In Australia, the federal government has entered into three agreements for the supply of vaccines, with roll-out beginning for the highest priority groups in February 2021. Expansion of the vaccination program throughout February and March failed to meet government targets and this has been attributed to international supply issues. However, Australia has local capacity to manufacture one million doses of the AstraZeneca vaccine weekly and once fully operational this will greatly increase the national vaccination capacity. Under current plans, these vaccine doses will be distributed primarily through a network of general practices, to be joined in later phases by community pharmacies. It remains unclear whether these small distribution venues have the logistical capacity to administer vaccines at the rate they will become available. To inform this discussion, we applied stochastic queue network models to estimate the capacity of vaccination sites based on assumptions about appointment schedules, service times and available staff numbers. We specified distinct queueing models for two delivery modes: (i) mass vaccination hubs located in hospitals or sports arenas and (ii) smaller clinics situated in general practices or community pharmacies. Based on our assumed service times, the potential daily throughput for an eight hour clinic at a mass vaccination hub ranged from around 500 vaccinations for a relatively small hub to 1,400 vaccinations a day for a relatively large hub. For GP vaccination clinics, the estimated daily throughput ranged from about 100 vaccinations a day for a relatively small practice to almost 300 a day for a relatively large practice. Stress tests showed that for both delivery modes, sites with higher staff numbers were more robust to system pressures, such as increased arrivals or staff absences, and mass vaccination sites were more robust that GP clinics. Our analysis is accompanied by an interactive web-based queue simulation applet, which allows users to explore queue performance under their own assumptions regarding appointments, service times and staff availability. Different vaccine delivery modes offer distinct benefits and may be particularly appealing to specific population segments. A combination of expanded mass vaccination hubs and expanded GP vaccination is likely to achieve mass vaccination faster than either mode alone.