DEM based numerical studies have shown that the formation of instabilities in granular materials is a continuous process and is influenced by both internal inhomogeneity and imposed stress states. Present study explores the influence of two types of lateral boundary conditions, stress controlled flexible boundary and velocity controlled rigid boundary, on the mechanical behaviour and instability response of sand under biaxial shearing employing DEM. It is observed that the specimen with flexible boundary estimates higher deviator stress as compared to that of rigid boundary, which is attributed to the additional confinement induced by the flexible boundaries. Further, for dense specimens with flexible boundaries, bulging type deformation is noticed accompanied with shear bands; whereas, for rigid lateral boundaries, the specimen always retains the initial outer shape enforcing the particles to adapt the kinematics of the wall boundary. For loose specimens, diffused instability mode is observed with surficial bulging only for flexible boundaries. The instability responses are assessed with the help of microlevel interaction at particle scale and evolution of meso-structure.