The simple procedure of calculating the infrared spectra of polymers is presented. It is based on selecting the relevant, medium-size representative fragments of a polymer, for which the vibrational frequencies are computed within the harmonic approximation, in conjunction with the multiparameter scaling techniques. Scaling is necessary to predict the reliable fundamentals, which, along with the calculated intensities and properly chosen band widths, reproduce the observed band shapes with high accuracy. Applications to the three polymers: poly(methyl methacrylate), poly(vinyl acetate), and poly(isopropenyl acetate) are presented. The simulated spectra are in good agreement with the experiment. The assignment of bands is reported. The obtained results indicate strong delocalization of the vibrational modes within polymers, which is in accord with the most recent experimental finding [Macromolecules 2008, 41, 2494-2501]. Good agreement between the observed and the calculated spectra of deuterated PMMA confirms the correctness of our approach. The preliminary results obtained for the highly irregular macromolecular compound (vinyl-functionalized silica) are also shown.