A railway baseplate assembly comprising a baseplate (30), a cushioning pad (20) for lying beneath the baseplate (30), and means (10) for securing the baseplate (30) to an underlying rail foundation when the assembly is in use, wherein the said securing means (10) comprise a non-screw-threaded post member (12), which post member (12) extends, when in use, through holes (21, 31) provided in the baseplate (30) and cushioning pad (20) in such a way as to engage the said baseplate (30). The post member (12) and baseplate (30) may be such that engagement of the baseplate (30) with the post member (12) can be brought about by movement of the baseplate (30) relative to the post member (12) firstly in a direction substantially perpendicular to the plane of the baseplate (30) and towards the post member (12) so that the post member (12) extends through the hole (31) in the baseplate (30) and secondly in a direction substantially parallel to the plane of the baseplate so that the post member (12) engages the baseplate (30). The post member (12) is fastened, directly or indirectly, to the rail foundation and the post member (12), cushioning pad (20) and baseplate (30) may be such that the cushioning pad (20) and baseplate (30) can be brought into engagement with the post member (12) while the post member (12) is fastened to the rail foundation.