The method of transfer matrix which was recently developed by Kerner to treat the problem of electronic band structure of mixed linear was applied to the problem of vibration of atomic linear chain. It was shown that this method affords to the problem of calculating the eigenfrequency-distribution of several kinds o lattices, including disordered ones. The well-known results for regular monatomic and diatomic lattices, and the results which were obtained by Montroll and Potts for linear lattices containing a few impurity atoms, were rederived by the matrix method in a much simpler way. The eigenvalue equations for the lattices containing several impurities at arbitrarily given positions were then derived. In cases where the force-constant is not altered by impurities the formulas become so simple that we can obtain the eigenfrequencies without laborious calculations. It is also possible to derive in such cases a simple approximate eigenvalue equation for lattices containing impurities distributed completely at random. This equation indicates that the mode of change in the distribution of eigenfrequencies is qualitatively the same as in the case of one or two impurities. Monatomic lattice with a single hole and diatomic lattice with a single were treated as simple examples. An attempt to extend the matrix method to the case in which the next-nearest interaction between atoms is taken into account was also mentioned.