This thesis concerns a numerical investigation for the stabilization (delay of laminar-to-turbulent transition) of ows over a at plate with a meta-unit of a possible metamaterial. The type of instability studied is that due to small disturbances in an incompressible, two-dimensional boundary layer. The linear growth of the disturbance in the form of a wave (also called the Tollmien-Schlichting wave) was of particular interest. There is a newly emerging class of structures called "metamaterials" which are capable of controlling the properties of classical waves (electromagnetic/optical/acoustic). This thesis investigates whether or not one of these materials are capable of attenuating TS waves. A literature review was conducted on three types of metamaterials, namely those based on Helmholtz-resonators, membranes structures and phononic crystals. The mechanisms for which the three aforementioned metamaterials attenuate acoustic waves are resonance, anti-resonance and Bragg's scattering respectively. Based on the likelihood of successfully achieving damping of TS waves, the phononic crystal was chosen to be further studied…