An important feature for two dimensional Euler equation is the mixing of the vorticity. The mixing ``averages" the vorticity and can sometimes drive the flow towards an equilibrium. In a breakthrough work, Bedrossian and Masmoudi established this mechanism (inviscid damping) in a Gevrey neighborhood of Couette flow in the whole space. As an attempt to understand their work, we consider the inviscid damping near Couette flow in a periodic channel, when the perturbed vorticity is supported away from the boundary. We show that the inviscid damping takes place in this case as well, in a sharper space. Difficulty with extending such results to general shear flow and general boundary effects will also be briefly discussed. This is based on joint work with Alex Ionescu.