Polyethylene terephthalate (PET) could be considered for the packaging of vegetable oils taking into account the impact of its oxygen permeability on the oxidation of the oil and the migration of volatile organic compounds (VOC) from the polymer matrix. After accelerated aging tests at 40 °C for 10, 20, and 30 days, the headspace of three sunflower oils packed in PET with high density polyethylene caps was carried out using solid phase microextraction. VOCs such as benzene hydrocarbons, ethylbenzene, xylene isomers and diethyl phthalate were identified in vegetable oils by gas chromatography coupled to mass spectrometry. Chemometric tools such as principal components analysis (PCA), independent components analysis (ICA), and a multiblocks analysis, common components and specific weight analysis (CCSWA) applied to analytical data were revealed to be very efficient to discriminate between samples according to oil oxidation products (hexanal, heptanal, 2-pentenal) and to the migration of packaging contaminants (xylene).