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Optical spectra of chemical mixtures contain spectral information about the pure chemical components. For almost three decades, spectroscopists have been trying to develop methods for retrieving the spectra and estimating the concentrations of the pure components. A new algorithm of self-modeling mixture analysis for rapid and accurate data processing has been developed. The proposed method is based on the assumptions of interactive principal component analysis and pure wavelength selection. The success of mixture analysis depends upon a number of factors, such as correctly estimating the number of pure components and properly handling the signal-to-noise ratio and non-linear absorptions in the original spectra. The algorithm starts from the Principal Component Analysis (PCA). Number of pure components and experimental noise are then predicted from the secondary principal components (PC's). Pure wavelengths are selected by scaling the experimental noise and by processing the significant PC's instead of the original spectra to reduce the effective noise level. User interaction is available for optimizing pure wavelength selections. Near-infrared spectra of natural gas mixtures and mid-IR spectra of an esterification reaction were processed. Spectra of pure components were correctly extracted. Results for the new algorithm are compared to those of two traditional self-modeling methods. A modified algorithm using the method of Alternating Least Squares was implemented to handle highly overlapped natural gas spectra. Two-dimensional Fourier transform filtering technique for the background reduction was used as a data pretreatment assisting the self-modeling analysis of hyperspectral IR images. Unresolved LC-FTIR data were investigated with the use of pure wavelength based algorithm. Predicted spectra of pure components in a diet coke and an epoxy curing agent samples were compared with the standard spectra.