  In the present paper we propose a stellar model under the $f(\mathbb{T})$
gravity following the conjecture of Mazur-Mottola~[Report number: LA-UR-01-5067
(2001); Proc. Natl. Acad. Sci. USA 101 (2004) 9545] known in literature as {\it
gravastar}, a viable alternative to the black hole. This gravastar has three
different regions, viz., (A) Interior core region, (B) Intermediate thin shell,
and (C) Exterior spherical region. It is assumed that in the interior region
the fluid pressure is equal to a negative matter-energy density providing a
constant repulsive force over the spherical thin shell. This shell at the
intermediate region is assumed to be formed by a fluid of ultrarelativistic
plasma and the pressure, which is directly proportional to the matter-energy
density according to Zeldovich's conjecture of stiff fluid~[Zeldovich, Mon.
Not. R. Astron. Soc. 160 (1972) 1], does nullify the repulsive force exerted by
the interior core region for a stable configuration. On the other hand, the
exterior spherical region can be described by the exterior Schwarzschild-de
Sitter solution. With all these specifications we have found out a set of exact
and singularity-free solutions of the gravastar which presents several
physically interesting as well as valid features within the framework of
alternative gravity.
