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.

12 pages, 6 figures