The roof stability of steel melting furnaces, especially two-bath furnaces, governs their service lives between repairs. Continuous monitoring of the lining thickness during operation of a furnace enables us to study the type and rate of wear of various refractories in relation to service factors and to ensure troublefree operation of the furnace until dead banking is necessary.Despite research [1][2][3][4][5][6][7][8][9], no method has yet been devised for sufficiently accurately determining the residual thickness of the brickwork during a furnace campaign. The essence of the method is that the density of a flux of T quanta from an extended source depends on its dimensions. If the refractory brick is treated with a flux of thermal neutrons, then as a result of activation its component elements will act as an extended source (an element of the brickwork) which changes in length as the furnace is operated.Thus by finding the relation between the T-quantum flux density at the detection point and the length of the brickwork element, we can establish continuous monitoring of the thickness of the lining. The sensitivity of the method is increased if the activity is exponentially distributed along the brick, e ~x [10], where ,~ is a coefficient approximately equal to the coefficient of linear attenuation of 7 quanta from the radioactive isotope iron-59 in the material of the brickwork (in our case ~ ~ 0.1 cm -t) , and x is the length of the extended source in centimeters. This activity distribution is obtained by using cadmium screens of the appropriate configuration.To find the relation between the T-quantum flux density and the length of the extended source, the refractories, cut into several pieces in cross section, were irradiated in a flux of neutrons simultaneously