In this letter, we study the outage probability of intelligent reflecting surface (IRS) assisted full duplex two-way communication systems, which characterizes the performance of overcoming the transmitted data loss caused by long deep fades. To this end, we first derive the probability distribution of the cascaded end-to-end equivalent channel with an arbitrarily given IRS beamformer. Our analysis shows that deriving such probability distribution in the considered case is more challenging than the case with the phase-matched IRS beamformer. Then, with the derived probability distribution of the equivalent channel, we obtain the closed-form expression of the outage probability performance. It theoretically shows that the reflecting element number has a conspicuous effect on the improvement of the system reliability. Extensive numerical results verify the correctness of the derived results and confirm the superiority of the considered IRS assisted two-way communication system comparing to the one-way counterpart.
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