  The singularity of the black hole solutions obtained before in M{\o}ller's
theory are studied. It is found that although the two solutions reproduce the
same associated metric the asymptotic behavior of the scalars of torsion tensor
and basic vector are quite different. The stability of the associated metric of
those solutions which is spherically symmetric non singular black hole is
studied using the equations of geodesic deviation. The condition for the
stability is obtained. From this condition the stability of the Schwarzschild
solution and di Sitter solution can be obtained.
