Damping against moderate to high impact is important for variety of engineering and technological applications. While, conventionally, damping has been achieved by using soft, elastic, and viscoelastic composite materials of different kinds, here we show that thin elastic layers embedded with fluid-filled micro-channels can have several advantages not found in the conventional ones. These layers are either smooth, homogeneous, or are embedded with micro-channels of different diameters, either open to atmosphere or are filled with oil of desired viscosity. We sandwich these layers between a rigid substrate and a flexible aluminum foil and subject them to moderate impacting load by colliding with rigid spheres of steel of different diameter. These experiments show that the kinetic energy dissipates more for layers of smaller thickness and for the ones embedded with the fluid filled micro-channels. Furthermore, the dissipation increases with viscosity of the oil inside the channels until a critical viscosity is reached beyond which it decreases. These results suggest that the damping occurs via frictional dissipation at interfaces and the viscous dissipation of liquid inside the channels.