  This paper examines the structure of a gravitationally vacuum star (also
known as gravastar) in the background of ${f}(\Re,\mathcal{T}^{2})$ theory.
This hypothetical object can be treated as a substitute of a black hole, with
three regions: (i) the internal region, (ii) the intrinsic shell and (iii) the
outer region. We examine these geometries using Finch-Skea metric for radial
metric component along with particular $f(\Re,\mathcal{T}^{2})$ model. We
determine singularity-free solution for both the inner as well as thin-shell
domains. The smooth matching of the interior region with external Schwarzschild
spacetime is obtained through Israel matching constraints. Finally, we study
various characteristics of gravastar domains including equation of state
parameter, proper length, entropy, energy as well as surface redshift. It is
found that the compact gravastar structure is a viable alternate to the black
hole in the perspective of this gravity.
