A direct relationship between the x-ray intensity ratio and the concentration ratio for bulk and thin specimens has been established by use of a revised full-diffusion model of electron scattering. The suitable ionization cross section, the most important parameter influencing the accuracy of the calculated Cliff-Lorimer factors, has been found after comparing the experimental intensity ratio I(L)/I(K) of eight elements (from Ge to Sn) and I(M)/I(L) of six elements (from Sm to Bi) with the calculated values. The quantitative standardless EDS analysis of bulk samples obtained by this direct method is more satisfactory than the commercial indirect method which gives the composition through ZAF correction after calculating the intensity factors of pure elements. The quantitative standardless analysis of thin samples has been improved by the suitable cross section significantly. This method has been applied to the analysis of film on substrate either without any common element or with one common element (P-Si glass film on Si). It has also been used to calculate the intensity factors of pure bulk samples and the backscattering correction factor in Auger electron spectroscopy.