  $f(T)$ gravity offers an alternative context in which to consider
gravitational interactions where torsion, rather than curvature, is the
mechanism by which gravitation is communicated. We investigate the stability of
the Kasner solution with several forms of the arbitrary lagrangian function
examined within the $f(T)$ context. This is a Bianchi type--I vacuum solution
with anisotropic expansion factors. In the $f(T)$ gravity setting, the solution
must conform to a set of conditions in order to continue to be a vacuum
solution of the generalized field equations. With this solution in hand, the
perturbed field equations are determined for power-law and exponential forms of
the $f(T)$ function. We find that the point which describes the Kasner solution
is a saddle point which means that the singular solution is unstable. However,
we find the de Sitter universe is a late-time attractor. In general relativity,
the cosmological constant drives the the isotropization of the spacetime while
in this setting the extra $f(T)$ contributions now provide this impetus.
