To provide a cover structure for an internal combustion engine that allows lubricating oil to surely flow while preventing interference between ribs and a timing chain.

A cover structure for an engine E includes a chain case 30 that covers a cam timing chain 24. The chain case 30 includes: bolt insertion holes 31a, 31b provided in side edges 31, 32 and fastened to an engine body 10; a first rib 35 that protrudes from a wall 33 to the engine body 10 side, is provided inside the cam timing chain 24, and extends along in a cylinder axial direction; and a second rib 36 that protrudes from the wall 33 to the engine body 10 side, is provided between the side edge 32 and the first rib 35, and is inclined so as to be located at the lower part in the cylinder axial direction as going toward the first rib 35. The first rib 35 is formed higher than the second rib 36 and its lower end is located at the upper part in the cylinder axial direction of a crank sprocket 21. The upper end of the second rib 36 is formed higher than the halfway part in the length direction.