A precast plinth for supporting an associated object, such as a rail of a railway track, includes an elongated body made of a material including concrete. The plinth includes an upper face, a lower face, a first side face, a second side face and first and second end faces. The first and second side faces taper away from each other from the upper face to the lower face. A leveling hole can extend from the upper face to the lower face with a threaded leveling insert located in the leveling hole. A grout hole can extend from the upper face to a lower face in a spaced manner from the leveling hole.