The use of polymer materials in industry for product packaging is increasing. The presence of additives in the polymer matrix enables the modification or improvement of the properties and performance of the polymer, but these industries are concerned regarding the extractability of these additives. The quantification of these additives is particularly challenging because of the presence of these substances as contaminants in all the analytical equipment and the diversity of their physicochemical properties. In this context, a multi-residue analytical method was developed for the trace analysis of the twenty main additives (and their degradation products) authorized in plastic products such as pharmaceutical packaging (e.g., antioxidants, release agents, and light absorbers). This analytical method consisted of a solid phase extraction (SPE) followed by an analysis using ultra-high performance liquid chromatography coupled to a tandem mass spectrometer (UHPLC-MS/MS). A comparison of two ionization interfaces and the optimization of the extraction procedure were discussed. The influence of the quality of the solvent type (distilled versus not distilled) and the nature of the SPE cartridges (Polypropylene versus Teflon®) were demonstrated. The optimized method exhibited a quantification limit lower than 20 ng mL−1 and recoveries between 70 % and 120 % for all compounds. Finally, the method was validated according to the ICH directive and was subsequently applied to the extraction of polymers under different pH conditions and storage temperatures. To the best of our knowledge, this study presents the first methodology allowing the simultaneous quantification of 24 additives at low ng mL−1.