An optically transmissive light directing sheeting and a method of making the same are disclosed. The light directing sheeting includes a core sheet of an elastic material that can be laminated onto other surfaces or sandwiched between sheets of various rigid materials. The core sheet includes a plurality of deep and narrow parallel channels configured to direct light by means of a total internal reflection. The method includes a step of slitting of a soft, optically transmissive plastic sheet with a blade and forming at least one array of substantially parallel linear slits in a surface of the sheet, a step of stretching the sheet in a direction perpendicular to the linear slits, and a step of bonding the sheet to a different sheet of an optically transmissive, rigid material. Various light directing devices employing the light directing sheeting are also disclosed.