Concept of resolving set and metric basis has enjoyed a lot of success because of multipurpose applications both in computer and mathematical sciences. A system in which failure of any single unit, another chain of units not containing the faulty unit can replace the originally used chain is called fault-tolerant self-stable system. Recent research reveal that the problem of finding metric dimension is NP-hard and problem of computing the exact values of fault tolerant metric dimension seems to be even harder although some bounds can be computed rather easily. In the present article we compute closed formulas for the fault-tolerant metric dimension of gear, anti-web gear and anti-web graphs. We conclude that out of these only anti-web graph has constant fault-tolerant metric dimension.