Polyethylene-co-vinylacetate (EVA) films with different concentrations (3.5 wt% and 7 wt%) of essential oil constituents, carvacrol or cinnamaldehyde, were prepared and characterized by mechanical, antibacterial and antibiofilm properties. The incorporation of the compounds into copolymer films affected their elastic modulus, tensile stress and elongation at break. Carvacrol and cinnamaldehyde act as plasticizers which reduce the intermolecular forces of polymer chains, thus improving the flexibility and extensibility of the film. The analysis of the surface characteristics demonstrated that essential oil constituents lowered the contact angle values without causing any remarkable variation of the surface roughness. The films allowed progressive diffusion of the bioactive molecules and the kinetic of release was correlated with the damaging effect on bacterial growth. The kill curves proved that the film with essential oil constituents (7 wt%) had a significant bactericidal effect (reduction of 4 and 2 log CFU) against Staphylococcus aureus and Escherichia coli and a bacteriostatic effect against Staphylococcus epidermidis and Listeria monocytogenes (reduction of about 1 log CFU). With regard to biofilm formation the biomass formed on polymeric films surface was significantly reduced if compared with the pure copolymer control. The results were confirmed by fluorescence microscopy images by Live/dead staining. The reduction in the surface tension coupled to an inherent bactericidal property of carvacrol and cinnamaldehyde could in turn affect the initial attachment phase of bacteria and compromise the normal biofilm development.