  We study the future cosmological singularities in the framework of massive
gravity and minimal massive bigravity theory. In this regards, we consider the
possible classes of finite-time future singularities such as sudden, big rip,
big freeze and big brake singularities in the massive universe. In dRGT model
with an open expanding universe we obtain the sudden singularity in the future
at a finite-time which generally without taking account of any particular
realistic equation of state, is not avoidable and except the fluid density, all
dynamical physical quantities such as pressure approach to infinity. To
complete our study, we search the future cosmological singularities in the
context of minimal massive bigravity theory and we find that the cosmology of
this theory suffers from the sudden and big brake singularities, in which we
can see that the parameters of the model approaches to zero the sudden
singularity can be removed.
