This paper presents an analysis of the transverse vibration of a rotating cable-connected spacecraft in which the flexural rigidity of the connecting cable is retained in the analysis. The method of matched asymptotic expansions is used to solve the singular perturbation problem, which must be solved for the determination of the mode shapes and natural frequencies. The problem is complicated by the presence of the eigenvalues and the perturbation parameter (which is a measure of the cable slenderness) in the boundary conditions. The effects of flexural rigidity on the mode shapes are shown to be confined to boundarylayer regions near the cable ends, and the effects on natural frequencies are shown to grow rapidly with increasing mode number.