A numerical approach is proposed to compute the dynamic response of periodic structures with cyclic symmetry, and assemblies made up of these periodic structures. The wave finite element (WFE) method is used to describe the wave modes which occur around the circumferential direction of these periodic structures. Emphasis is placed on assessing the dynamic flexibility modes of a periodic structure by considering unit forces which are successively applied to the boundary degrees of freedom. It is shown that the matrices of dynamic flexibility modes can be quickly computed. This yields an efficient dynamic substructuring technique to analyze the dynamic behavior of assemblies made up of several periodic structures. Numerical experiments are carried out which concern the analysis of a single periodic structure as well as assemblies made up of two and three structures.