Abstract: ‍ ‍Given the increasingly complex communication scenarios and the scarcity of spectrum resources， along with the critical importance of information freshness， this paper proposes a full duplex two-way （FDTW） model that integrates Full Duplex （FD） and bidirectional relay technologies based on Short Packet Communication （SPC）. Utilizing the Age of Information （AoI） as a metric for measuring information freshness， three transmission schemes are designed： Non relay-assisted （NRA）， Amplify-and-forward relay-assisted （AFRA）， and Decode-and-forward relay-assisted （DFRA）. Mathematical models are developed using short packet transmission theory to analyze the average packet error rate at the destination node under each scheme. Graph decomposition methods are employed to compute the Average Age of Information （AAoI） for each scheme. Furthermore， considering the complexity of AoI evolution in relay-assisted schemes， Markov chain analysis is used as a supplementary method to graph decomposition， particularly under scenarios of transmission complexity. Simulation results demonstrate that relay assistance significantly reduces AAoI when the direct link channel conditions are poor. The optimal AAoI， approximately 220 bits， is achieved with the AFRA scheme， resulting in an 8.33% reduction. The DFRA scheme performs better in AAoI for small packet lengths， while the AFRA scheme outperforms the others when the packet lengths exceed 160~180 bits. Additionally， the overall AAoI decreases as the direct link conditions improve.