A railway rail pad (1), for use beneath a railway rail in a rail fastening assembly as cushioning and/or electrical insulation, has first and second major faces (2, 3), the first face (2) having a rail seat portion (20) on which a foot of a railway rail sits when the pad (1) is in use, and side members (4A, 4B) attached to and extending from two opposite edges of the first face (2) of the pad (1). The side members (4A, 4B) are arranged so as to be located on respective opposite sides of the railway rail when the pad (1) is in use such that the rail seat portion (20) of the pad (1) lies between respective inwardly-facing wall faces (41A, 41B) of the said side members (4A, 4B). When the pad (1) is not under load and is placed so as to rest on a surface with the first face (2) of the pad (1) uppermost and part of the surface lying beneath the rail seat portion of the pad, an inclination angle (α1, α2) between the wall face (41A, 41B) of each side member (4A, 4B) and that part of the surface beneath the rail seat portion on which the pad (1) is resting is greater than 90°. When the pad is not under load, the first face is substantially convex in a vertical plane that is perpendicular to the longitudinal axis of the rail when the pad is in use.