We consider the 2-dim capillary gravity water wave problem -- the free boundary problem of the Euler equation with gravity and surface tension -- of finite depth $x_2 \in (-h, 0)$ linearized at a uniformly monotonic shear flow $U(x_2)$. We provide a complete picture of the eigenvalue distribution and prove the linear inviscid damping near monotone shear flow under some certain conditions. This is a joint work with Chongchun Zeng.