  In this paper, we have analyzed the stability of cylindrically symmetric
collapsing object filled with locally anisotropic fluid in $f(R,T)$ theory,
where $R$ is the scalar curvature and $T$ is the trace of stress-energy tensor
of matter. Modified field equations and dynamical equations are constructed in
$f(R,T)$ gravity. Evolution or collapse equation is derived from dynamical
equations by performing linear perturbation on them. Instability range is
explored in both Newtonian and post-Newtonian regimes with the help of
adiabetic index, which defines the impact of physical parameters on the
instability range. Some conditions are imposed on physical quantities to secure
the stability of the gravitating sources.
