There are provided a light source device and a display device which do not generate a wrinkle on an optical sheet even if the optical sheet is held on an LED substrate. A reflection sheet 11 is disposed between each of head portions possessed by a rivet, a positioning rivet and a support rivet and one surface of an LED substrate 8 where an LED is mounted, and a gap in a direction of a sheet thickness is provided between the head portion of each of the rivets and the reflection sheet 11. In the case in which a sudden thermal change is caused, therefore, the reflection sheet 11 expands or contracts between the head portion of each of the rivets and the reflection sheet 11 so that the wrinkle can be prevented from being generated over the reflection sheet 11.