Plastic materials are massively present in technological, industrial, and everyday applications, with increasing concern in toxicological aspects for health and environment. Characterization becomes an important issue as the structural, size and textural properties of plastics are needed to identify and track their life, from their production to their eventual degradation. Raman spectroscopy appears as a key tool for characterizing a wide variety of materials including plastics. It is fast, robust, sensitive to nanosized and amorphous particles. In order to be properly used for plastics, the Raman response of reference materials needs to be carefully assessed, the literature on such assessments being scarce. In this work, we attempt to fill this gap by employing theoretical calculations to generate ab initio spectra on the reference material polystyrene. The goal is to explain the origin of the peaks and their robustness to map the Raman response on controlled composition and structure, using linear ordered polymeric and finite amorphous models. The CRYSTAL package has been used to obtain full Raman spectra (vibrations, intensity) based on a careful benchmark of computational settings of functional and basis set. Whereas some peaks are found to be present in all the spectra and could be used for calibration purposes, other peaks are structure dependent and could be used to identify the type of polymer. We conclude that Raman spectroscopy is a technique well suited for the study of plastics, provided that a careful analysis of the origin of signal is done to fully interpret the spectra and deploy applications.