A method and strand guide for supporting, guiding and cooling casting strands (1) made of steel, especially preliminary sections (2) for girders, which are cooled by injected water (29) and are drawn, serve to prevent cracks, especially surface cracks, from appearing in the microstructure by adapting the cooling conditions of the surface of the strand in the region of the secondary cooling, and serve to prevent undercooling of the strand shell, wherein in order to avoid an undesirable solidification structure on the upper flange edges or in other cross-sectional areas, the cooling and support of the beam blank format are so adapted to the solidification range that cooling and support are provided exclusively where a crater is formed. To this end, the casting strand (1) is cooled, by guiding the temperature in a specific manner in upper supporting segments (5, 6, 7), by means of spray-water jets the width of which at least matches the length of the supporting rollers on longitudinal and transversal sides (13, 14) of the cross section (1a) of the casting strand, and is decreasingly supported in an analogous manner with respect to the length of the casting path and the cooling state in core areas (15) of the cross section (1a) of the casting strand on the transversal sides (14) of said casting strand cross-section (1a) so that cooling occurs exclusively by means of water jets (8) which are oriented towards said core areas (15).