<p><b>Abstract</b>—This paper proposes a cut-based technique to compute bounds on the full access probability of an extra stage shuffle exchange network (<tmath>$ESEN$</tmath>) and a wrap-around inverse banyan network (<tmath>$WIBN$</tmath>). Note that the problem of finding an exact full access probability is known to be NP-hard. Our results obtain tighter bounds as compared to those using existing techniques. For a small size multistage interconnection network, it deviates less from the exact value. We also notice that our proposed lower bound is conservative. Further, the lower bound is important as it suggests that a network is at least this much reliable.</p>