  We present a detailed study of the Vaidya solution and its generalization in
de Rham-Gabadadze-Tolley (dRGT) theory. Since the diffeomorphism invariance can
be restored with the St\"{u}ckelberg fields $\phi^a$ introduced, there is a new
invariant $I^{ab}=g^{\mu \nu}\partial_\mu \phi^a\partial_\nu \phi^b$ in the
massive gravity, which adds to the ones usually encountered in general
relativity. There is no conventional Vaidya solution if we choose unitary
gauge. In this paper, we obtain three types of self-consistent ansatz with some
nonunitary gauge, and find accordingly the Vaidya, generalized Vaidya and furry
Vaidya solution. As by-products, we obtain a series of furry black hole. The
Vaidya solution and its generalization in dRGT massive gravity describe the
black holes with a variable horizon.
