  We obtain the equations of motions of the $f(T)$ theory considering the
Lema\^itre-Tolman-Bondi's metric for a set of diagonal and non-diagonal
tetrads. In the case of diagonal tetrads the equations of motion of the $f(T)$
theory impose a constant torsion or the same equations of the General
Relativity, while in the case of non-diagonal set the equations are quite
different from that obtained in GR. We show a simple example of an universe
dominated by the matter for the two cases. The comparison of the mass in the
non-diagonal case shows a sort of increased with respect to the diagonal one.
We also perform two examples for the non-diagonal case. The first concerns a
black hole solution of type Sshwarzschild which presents a temperature higher
than that of Schwarzschild, and a black hole in a dust-dominated universe.
