The calyx of Held is a giant glutamatergic synapse in the auditory system and displays multiple forms of short-term facilitation and depression. This study presents a detailed model of short-term plasticity at this synapse. The main components of the model are the presynaptic vesicle dynamics, which include passive and activity-dependent recycling, calcium-dependent exocytosis and the postsynaptic AMPA receptor kinetics. The behaviour of the model is compared to experimental data and reproduces the time course and amplitude of synaptic depression during repetitive stimulation at different frequencies. A comparison of different manipulations of the model shows that accurate fits require the inclusion of fast activity-dependent vesicle recycling and a limited number of vesicle docking sites at each active zone.