  We study the Coleman-de Luccia (CDL) instanton characterizing the tunneling
from a false vacuum to the true vacuum in a semi-classical way in dRGT
(deRham-Gabadadze-Tolley) massive gravity theory, and evaluate the dependence
of the tunneling rate on the model parameters. It is found that provided with
the same physical Hubble parameters for the true vacuum $H_{\rm T}$ and the
false vacuum $H_{\rm F}$ as in General Relativity (GR), the thin-wall
approximation method implies the same tunneling rate as GR. However, deviations
of tunneling rate from GR arise when one goes beyond the thin-wall
approximation and they change monotonically until the Hawking-Moss (HM) case.
Moreover, under the thin-wall approximation, the HM process may dominate over
the CDL one if the value for the graviton mass is larger than the inverse of
the radius of the bubble.
