In this work, we investigate the physical layer security (PHYLS) performance of full-duplex (FD) cellular networks, where the downlink (DL) and uplink (UL) occur over the same radio-frequency (RF) resources. Here, the locations of the base stations (BSs) and mobile terminals (MTs) are drawn from stationary Poisson point processes (PPPs). Moreover, the eavesdroppers (EDs) locations are unknown to the network, and are thus modeled from an independent PPP. We characterize the signal-to-interference-plus-noise ratio (SINR) distributions at the reference BS, MT, and most malicious EDs. Accordingly, we develop explicit expressions for the secrecy rates in both UL and DL of the FD cellular network under consideration. Our finding show that the choice of FD versus HD operation, in addition to improving the spectral efficiency, can enhance the secrecy rate, particularly for ultra-dense deployments.