  This paper is devoted to study the stability/instability of the expansionfree
self gravitating source in the framework of Einstein Gauss-Bonnet gravity. The
source has been taken as Tolman-Bondi model which is homogenous in nature. The
field equations as dynamical equations have been evaluated in Gauss-Bonnet
gravity in five dimensions. The junction conditions as well as cavity
evaluations equations have been explored in detail. The perturbation scheme of
first order has been applied to dynamical as Einstein Gauss-Bonnet field
equations. The concept of Newtonian as well post Newtonian approximation have
been used to derive general dynamical stability equations. In general this
equation represents the stability of the gravitating source. Some particular
values of system parameters have been chosen to prove the concept of stability
graphically. It has been mentioned that other than chosen the particular values
of the parameters the stability of the system would be disturbed, hence it
would leads to instability.
