Spectrum scarcity and dramatically increasing demand for high data rate and high‐quality video live streaming are of future cellular network design challenges. As a solution to this problem, cache‐enabled cellular network architecture has been recently proposed. Device‐to‐device (D2D) communications can be exploited for distributed video content delivery, and devices can be used for caching of the video files. This can increase the capacity and reduce the end‐to‐end delay in cellular networks. In this study, the authors propose a new scheme for video distribution over cellular networks by exploiting full‐duplex (FD) radios for D2D devices in two scenarios: (i) two nodes exchange their desired video files simultaneously and (ii) each node can concurrently transmit to and receive from two different nodes. In the latter case, an intermediate transceiver can serve one or multiple users’ file request(s) whilst capturing its desired file from another device in the vicinity. Mathematical expressions along with extensive simulations are used to compare their proposed scheme with a half‐duplex scheme to show the achievable gains in terms of sum throughput, active links, and delay. They will also look into the energy cost for achieving the improvements provided by operation in FD mode.