AbstractThe simultaneous iteration method of obtaining eigenvalues and eigenvectors is employed for the solution of undamped vibration problems. This method is of significance when a few of the dominant eigenvalues and eigenvectors are required from a large matrix, and hence is particularly suitable for vibration problems involving a large number of degrees of freedom. It is shown that advantage may be taken of both the symmetry and the band form of the mass and stiffness matrices, thus making it feasible to process on a computer larger order vibration problems than can be processed using transformation methods. A method of allowing for body freedom is given and some numerical tests are discussed.