With the use of high-resolution and high-quality spectra, 31 yellow supergiants of the Large (LMC) and Small (SMC) Magellanic Clouds are investigated through the method of atmosphere modeling. The abundance values for 20 chemical elements are determined. It is shown that alpha-elements are in a slight excess and neutron-capture elements have an excess up to 0.60 dex. The approbation of a new method for the determination of absolute stellar magnitudes of supergiants of late spectral types is performed. The method is based on the employment of the spectroscopic criteria, namely, the depth-line ratios for iron. Absolute stellar magnitudes of nine LMC supergiants are calculated using this method. The value of the LMC distance modulus is estimated: m - M = 18.4 ± 0.3^m.