  In this paper, Killing vectors of spherically spacetimes have been evaluated
in the context of teleparallel theory of gravitation. Further, we investigate
the Killing vectors of the Friedmann metrics. It is found that for static
spherically spacetimes the number of Killing vectors turn out to be
\emph{seven} while for the Friedmann models, we obtain \emph{six} teleparallel
Killing vectors. The results are then compared with those of General
Relativity. We conclude that both of these descriptions of gravity do not
provide the consistent results in general. However, these results may coincide
under certain conditions for a particular spacetime.
