  Metastable cosmic strings appear in models of new physics with a two-step
symmetry breaking $G\to H\to 1$, where $\pi_1(H)\neq 0$ and $\pi_1(G)=0$. They
decay via the monopole-antimonopole pair creation inside. Conventionally, the
breaking rate has been estimated by an infinitely thin string approximation,
which requires a large hierarchy between the symmetry breaking scales. In this
paper, we reexamine it by taking into account the finite sizes of both the
cosmic string and the monopole. We obtain a robust lower limit on the tunneling
factor $e^{-S_B}$ even for regimes the conventional estimate is unreliable. In
particular, it is relevant to the cosmic string interpretation of the
gravitational wave signals recently reported by pulsar timing array
experiments.
