A railway rail support assembly (3), for resiliently suspending a railway rail (1) above a track foundation (2) at discrete locations along the rail (1), has rail supporting means through which a predetermined clamping load is exerted on the said rail (1) such that the assembly (3) has a desired resistance to longitudinal creep therethrough of the rail (1). The rail supporting means are preferably attached, when the assembly (3) is in use, to an approximately horizontal upper surface of the said track foundation (2). Such an assembly (3) may be provided by first and second brackets (31, 32) and first and second elastic members (33, 34). Each of the said first and second brackets (31, 32) has a bearing part (312, 322) and a base part (311, 321) (311, 321), the bearing part (312, 322) being located adjacent to either sides of the rail (1) when the assembly (3) is in use and the base part (311, 321) being located on an upper surface of the said track foundation (2). The first elastic member (33) is located between the first bracket (31) and the rail (1) and the second elastic member (34) is located between the rail (1) and the second bracket (32), when the assembly (3) is in use. The assembly (3) further comprises means for maintaining the said predetermined clamping load.