The structure of estrogen receptors and their interaction with 17beta-estradiol and estriol are of particular interest today because the treatment of breast cancer and the cause of the disease are intricately linked to the activity of the estrogen receptor and the normal blood serum level of these hormones. Molecular geometry and vibration frequencies of these steroid hormones are calculated by density functional theory with the B3LYP/ 6-31G** approximation. Intensities of infrared absorption and Raman spectra for estradiol are in an agreement with the experiment data. The assignments of all vibrational bands in the spectra of these hormones are presented on the basis of quantum chemical calculations of frequencies and normal modes. For the large number of bands such an assignment is made for the first time. The analysis of infrared spectra of both hormones indicates some nontrivial structure-spectra correlations. A series of specific vibrations is predicted in the low-frequency region of the IR spectra; their role in hormone-receptor interaction and in energy transfer processes are discussed. The search of the optimized geometrical structure by minimization of the total energy gradient is accompanied by the second derivatives calculation; diagonalization of the Hessian matrix leads finally to solution of vibration problem. The 17beta-estradiol molecule consists of 44 atoms and has 126 normal modes of internal vibrations. All these normal modes are presented together with their analysis and comparison with experimental data. From this comparison we have obtained an assignment of all absorption IR bands of 17beta-estradiol recorded earlier in KBr. For all stretching vibrations our assignment is in agreement with the previous one, obtained on the basis of the empirical rules. Direct DFT calculation of vibrational frequencies cannot provide a 100% agreement with the experimental IR spectra and scaling factors in the range of 0.95-0.97 are used in order to fit theoretical and experimental data.