To respond to bioterrorism events or to curb outbreaks of contagious diseases, county health departments must set up and operate clinics to dispense medications or vaccines. Planning these clinics in advance of such an event requires determining clinic capacity and estimating the queueing that may occur in such facilities. We construct a queueing network model for mass dispensing and vaccination clinics and estimate the time that residents will spend at each workstation in such facilities. A key contribution is the development of useful approximations for queueing systems that have batch arrival, multiple-server batch processes and self-service stations. We compared the model’s estimates to those from simulation experiments of realistic clinics using data collected from emergency preparedness exercises. Although this research was motivated by this specific application, the model should be applicable to the design and analysis of other similar queueing networks, including manufacturing systems with batch processes.