  This paper explores stability of the Einstein universe against linear
homogeneous perturbations in the background of $f(\mathcal{G},T)$ gravity. We
construct static as well as perturbed field equations and investigate stability
regions for the specific forms of generic function $f(\mathcal{G},T)$
corresponding to conserved as well as non-conserved energy-momentum tensor. We
use the equation of state parameter to parameterize the stability regions. The
graphical analysis shows that the suitable choice of parameters lead to stable
regions of the Einstein universe.
