Polycryst. diamond films were deposited by hot filament assisted chem. vapor deposition on five metal and insulator substrates. The films obtained were studied by Raman spectroscopy. The position of the Raman line shifts to higher wavenumbers when the thermal expansion coeff. of the substrate material increases. This effect is interpreted as a result of the internal stress in the diamond films induced by the cooling from the deposition temp. to room temp. The width of the Raman peak ranges from 10.9 to 16.6 cm-1, with a min. when the thermal expansion coeff. of the substrate is close to that of diamond.