The vibrational properties of polymers adsorbed on surfaces are investigated within the frame of two simple models. First the surface is modelled as a onedimensional infinite harmonic chain. Polymeric " molecules " are represented as harmonic chains of finite length. The coupling between the polymers and the surface is treated within the frame of the Interface Response Theory. Upon adsorption of polymers, resonant vibrational modes appear as well defined peaks in the variation of the density of states of the system. The effect of the interaction between adsorbed polymers via phonons is investigated and shown to lead to antiresonances in the spectral density of states and the formation of gaps in the density of states as the surface coverage is increased. A second more realistic model is introduced where the same finite harmonic chains (polymers) are grafted on a two dimensional [OOl] surface cut through a cubic harmonic crystal. Again the variation in density of states exhibits resonant modes between the polymers and the substrate. However, in this case, the interaction between polymers is short range. Adsorption of a film of polymers produces resonant modes which remain well-defined features within the substrate bulk band.