  We investigate linear and non-linear dynamics of spherically symmetric
perturbations on a static configuration in scalar-tensor theories focusing on
the chameleon screening mechanism. We particularly address two questions: how
much the perturbations can source the fifth force when the static background is
well screened, and whether the resultant fifth force can change the stability
and structure of the background configuration. For linear perturbations, we
derive a lower bound for the square of the Fourier mode frequency $\omega^2$
using the adiabatic approximation. There may be unstable modes if this lower
bound is negative, and we find that the condition of the instability can be
changed by the fifth force although this effect is suppressed by the screening
parameter. For non-linear perturbations, because we are mainly interested in
short wavelength modes for which the fifth force may become stronger, we
perform numerical simulations under the planar approximation. For a
sufficiently large initial amplitude of the density perturbation, we find that
the magnitude of the fifth force can be comparable to that of Newtonian gravity
even when the model parameters are chosen so that the static background is well
screened. It is also shown that if the screening is effective for the static
background, the fluid dynamics is mostly governed by the pressure gradient and
is not significantly affected by the fifth force.
