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We investigate linear and non-linear dynamics of spherically symmetricperturbations on a static configuration in scalar-tensor theories focusing onthe chameleon screening mechanism. We particularly address two questions: howmuch the perturbations can source the fifth force when the static background iswell screened, and whether the resultant fifth force can change the stabilityand structure of the background configuration. For linear perturbations, wederive a lower bound for the square of the Fourier mode frequency $\omega^2$using the adiabatic approximation. There may be unstable modes if this lowerbound is negative, and we find that the condition of the instability can bechanged by the fifth force although this effect is suppressed by the screeningparameter. For non-linear perturbations, because we are mainly interested inshort wavelength modes for which the fifth force may become stronger, weperform numerical simulations under the planar approximation. For asufficiently large initial amplitude of the density perturbation, we find thatthe magnitude of the fifth force can be comparable to that of Newtonian gravityeven when the model parameters are chosen so that the static background is wellscreened. It is also shown that if the screening is effective for the staticbackground, the fluid dynamics is mostly governed by the pressure gradient andis not significantly affected by the fifth force.

Dynamical Analysis of Screening in Scalar-Tensor Theory