The stability of the Einstein static universe against the homogeneous scalar perturbations in f ( T ) gravity is analyzed .
Both the spatial closed and open universes are considered .
We find that the stable Einstein static solutions exist in both cases .
Considering a concrete f ( T ) model and assuming that the cosmic energy has a constant equation of state w , we obtain that , in the closed case , w < 1 / 3 is required .
Thus , f ( T ) theory gives a larger region of w than that in general relativity ( -1 < w < -1 / 3 ) to have the stable Einstein static solution .
For the open universe , f ( T ) theory allows the stable Einstein static solution , although this kind of solution is forbidden in general relativity .
Thus , a modification of gravity can play a crucial role in stabilizing the Einstein static solution .