This paper consists of three sections. In the first section an efficient method is used for decomposition of the canonical matrices associated with repetitive structures. to this end, cylindrical coordinate system, as well as a special numbering scheme were employed. In the second section, divide and conquer method have been used for eigensolution of these structures, where the matrices are in the block tri-diagonal form. In the third section a comparison of the results is presented. In order to illustrate the efficiency of the aforementioned methods, repetitive structures are considered in the form of barrel vault space structures.