Abstract: To produce tubes of reactive metals, a melt (14) is removed from the annu gap (13) of a crucible (10). The temperature of the melt (14) is such as to ensure the formation of the solidus-liquidus zone (33) directly behind the annular gap (13), a planar solidification front (34) being created in a non supported region which is not exposed to the direct influence of a cooling means. In the subsequent region, the oriented solidification of the tube with high temperature gradients is realized, and the tube can be shaped or adjusted free of thermal influences. Only thereafter, the tube (25) is exposed to the action of cooling means (26, 31) to cool it without contact. In such a way, it is possible to produce tubes having a high stability and resistance to temperatures for use in turbines, heat exchangers or the like.