Spectral simulations of polarized attenuated total reflection (ATR) spectra have been used to quantitatively determine the orientation of alpha -helical polypeptides. Transmittance and polarized ATR spectra of five monolayers of poly-gamma -benzyl-L-glutamate (PBG) transferred by the Langmuir-Blodgett techniques on germanium crystal have been recorded, and the dichroic ratios of the amide I and amide II bands have been calculated. Simulations were performed using anisotropic optical constants of PEG in the molecular coordinate system and using the 4 x 4 matrix formalism of Berreman. Assuming that the alpha -helices are parallel to the plane of the ATR crystal, an average angle of 38 degrees +/- 1 degrees between the helix axes and the withdrawing direction has been found. Simulated spectra for various orientations of the alpha -helices are then given and influence of the azimuthal and tilt angles on the dichroic ratios of the amide bands has been investigated.