  We investigate models of future finite-time singularities in $f(T)$ theory,
where $T$ is the torsion scalar. The algebraic function $f(T)$ is put as the
teleparallel term $T$ plus an arbitrary function $g(T)$. A suitable expression
of the Hubble parameter is assumed and constraints are imposed in order to
provide an expanding universe. Two parameters $\beta$ and $H_s$ that appear in
the Hubble parameter are relevant in specifying the types of singularities.
Differential equations of $g(T)$ are established and solved, leading to the
algebraic $f(T)$ models for each type of future finite time singularity.
Moreover, we take into account the viscosity in the fluid and discuss three
interesting cases: constant viscosity, viscosity proportional to $\sqrt{-T}$
and the general one where the viscosity is proportional to $(-T)^{n/2}$, where
$n$ is a natural number. We see that for the first and second cases, in
general, the singularities are robust against the viscous fluid, while for the
general case, the Big Rip and the Big Freeze can be avoided from the effects of
the viscosity for some values of $n$.
