  The aim of this paper is to perform stability analysis of anisotropic
dissipative cylindrical collapsing model in $f(R,T,R_{\mu\nu} T^{\mu\nu})$
gravity. In this context, the modified version of hydrodynamical equation is
explored by means of dynamical equations and radial perturbation scheme. We
examined the role of adiabatic index, dissipation as well as the particular
cosmological model on the onset of dynamical instability of the evolving
cylindrical system that was initially in hydrostatic equilibrium with Newtonian
and post Newtonian approximations. It is pointed out that extra curvature terms
of $f(R,T,R_{\mu\nu}T^{\mu\mu\nu})$ gravity tends to increase the stability,
while that heat radiations push the system to enter into unstable window.
Further, our results reveal the significance of adiabatic index in the
stability analysis of cylindrical celestial model.
