Recent investigations in nanotechnology show that carbon nanotubes have significant mechanical, electrical and optical properties. Interactions between those are also promising in both research and industrial fields. Those unique characteristics are mainly due to the atomistic structure of carbon nanotubes. In this paper, the structural effects of vacant atoms on single walled carbon nanotubes are investigated using matrix stiffness method. In order to use this technique, a linkage between structural mechanics and molecular mechanics is established. A code has been developed to construct the single walled carbon nanotubes with the desired chirality, extracting the vacant atoms with the corresponding atomic bonds between the neighbor nodes and calculating the effect of these vacancies on their vibrational properties. In order to investigate the effect of those vacant nodes, large number of simulations has been carried out with randomly positioned vacant atoms. Also, consecutive vacant nodes have been positioned in order to investigate their effect on the structural properties through the length of a single walled carbon nanotubes. Effects of vacancies on Young's modulus have also been investigated. It is concluded that any amount of vacant atoms have substantial effect on modal frequencies and modulus of elasticity. Chirality and the amount/position of the vacancies are the main parameters determining the structural properties.