An attempt is made to apply the Green's function procedure to the case of linear XYZ type molecules. The isotopic rules have been formulated. The potential energy constants and mean amplitudes of vibrations of the various molecules of the linear XYZ type have been determined. The force constants of the different groups are discussed in the light of the ionic character or electronegativities taking recourse to the resonance structures wherever possible. The coriolis ζ sum rule for the linear XYZ type molecules have been verified. The rotational distortion constant Dj for the linear XYZ type molecules were determined and the calculated values were compared with the experimental values for the case of HCN, DCN, BrCN, ICN, NNO and OCS molecules.