We have developed a method for using near infrared Raman spectroscopy to quantitatively analyze the histochemical composition of human artery. The main contributors to bands observed in the Raman spectra of normal and atherosclerotic aorta are the proteins collagen and elastin, cholesterol lipids, and calcium hydroxyapatite. The Raman scattering cross-sections of different bands for these components have been determined in order to understand their relative contributions to the Raman spectra of biological tissue. The Raman signal is observed to behave linearly with the concentration of the components, even in a highly scattering medium such as a powder. Using these data, we have developed a linear model that can be used to extract the quantitative contribution of an individual component to the spectrum of a mixture. The model has been applied to several mixtures of known composition of tissue constituents in order to evaluate its precision and accuracy. The calculated fit coefficients from the spectra are in agreement with the measured values within experimental uncertainties. The spectra of different types of atherosclerotic aorta have also been modeled, and we have extracted quantitative information regarding the relative concentration of biological constituents in atherosclerotic aorta.