With fluorescent X-ray analysis as routine work, the correction term for the coexistent element can be expressed as linear terms of the weight fraction of the element because the compositions of samples are limited to a small range. Usually those correction factors which require a great deal of work are obtained experimentally. The authors have obtained theoretical equations of fluorescent X-ray intensity which are in good agreement with experimental values. The linear correction factors are obtained from derivatives of those equations, and their values can be easily calculated with a computer. The experimental X-ray intensity versus the weight fractions is usually expressed as a line. However, the linear approximation is not correct over a wide range of the composition. The second derivative of the theoretical equation explains the deviation from the linear approximation and gives the range where the linear approximation is allowed. The calculations are applied to the analysis of stainless steels, several low-alloy steels, and iron ores, and experimental results are corrected by the calculated results. Correction factors for Ni Kα, Fe Kα, Cr Kα, Mn Kα, and Cu Kα in stainless steels and Cr Kα and Mn Kα in low-alloy steels are calculated for coexistent elements such as carbon, silicon, titanium, chromium, manganese, copper, niobium, and molybdenum. For example, standard deviations of chromium and manganese analyzed results in lowalloy steels decrease from 0.169 and 0.044% to0.030 and0.023%, respectively, with theoretical corrections. In the analysis of iron ore, the fluorescent X-ray intensity of iron is affected by combined oxygen, which is different for the various compounds of iron oxides, and other impurities such as alumina, silica, and lime. The correction factors of these are obtained by calculation, and the standard deviation decreases from 1.70 to 0.44% for 55.1 to 68.5% iron. It is found by experiment that the theoretical values have about 1 or 2% of relative errors, and their derivatives also have relative errors of the same order of magnitude. But the ranges of coexistent elements are usually small, a few percent at most in routine work, and the theoretical values can be used in practical analyses.