  We study the stability of the Vainshtein screening solution of the
massive/bi-gravity based on the massive nonlinear sigma model as the effective
action inside the Vainshtein radius. The effective action is obtained by taking
the $\Lambda_2$ decoupling limit around a curved spacetime. First we derive a
general consequence that any Ricci flat Vainshtein screening solution is
unstable when we take into account the excitation of the scalar graviton only.
This instability suggests that the nonlinear excitation of the scalar graviton
is not sufficient to obtain a successful Vainshtein screening in
massive/bi-gravity. Then to see the role of the excitation of the vector
graviton, we study perturbations around the static and spherically symmetric
solution obtained in bigravity explicitly. As a result, we find that linear
excitations of the vector graviton cannot be helpful and the solution still
suffers from a ghost and/or a gradient instability for any parameters of the
theory for this background.
