A rail assembly in which the shanks of a rail between the head and the base have one pair of outwardly facing downwardly tapering flank surfaces and a frame flanking the rail has a pair of downwardly tapering inwardly facing flank surfaces spaced from and juxtaposed with the surfaces of the rail. The surfaces receive between them under precompression so as to generate a spring constant of 2 KN/mm to 8 KN/mm per meter of rail length, elastic intermediate layers which resiliently support the rail. One of the pairs of surfaces is composed of angularly adjoining upper and lower portions while the other is rectilinear over the height thereof juxtaposed with the first mentioned pair.