Working Memory (WM) is a cognitive mechanism that enables temporary holding and manipulation of information in the human brain. This mechanism is mainly characterized by a neuronal activity during which neuron populations are able to maintain an enhanced spiking activity after being triggered by a short external cue. In this study, we implement, using the NEST simulator, a spiking neural network model in which the WM activity is sustained by a mechanism of short-term synaptic facilitation related to presynaptic calcium kinetics. The model, which is characterized by leaky integrate-and-fire neurons with exponential postsynaptic currents, is able to autonomously show an activity regime in which the memory information can be stored in a synaptic form as a result of synaptic facilitation, with spiking activity functional to facilitation maintenance. The network is able to simultaneously keep multiple memories by showing an alternated synchronous activity which preserves the synaptic facilitation within the neuron populations holding memory information. The results shown in this study confirm that a WM mechanism can be sustained by synaptic facilitation.