  We explore the relic abundance of asymmetric Dark Matter in shear--dominated
universe in which it is assumed the universe is expanded anisotropically. The
modified expansion rate leaves its imprint on the relic density of asymmetric
Dark Matter particles if the asymmetric Dark Matter particles are decoupled in
shear dominated era. We found the relic abundances for particle and
anti--particle are increased. The particle and anti--particle abundances are
almost in the same amount for the larger value of the shear factor $x_e$ which
makes the indirect detection possible for asymmetric Dark Matter. We use the
present day Dark Matter density from the observation to find the constraints on
the parameter space in this model.
