The vibration of tensioned cables with flexural rigidity is analyzed in terms of power transmission past a slender rigid body using an exact wave-based method. It is assumed that the cable is made from a linear elastic material, is perfectly straight, and in a vacuum. The results are presented in terms of nondimensional frequency, rigid body mass, and critical frequency at which membrane and flexural stiffness contributions are equal. The results show that transmission is affected as low as a decade below the critical frequency. Flexural rigidity increases the effective bandwidth of transmission and the rocking resonance frequency and is therefore an important consideration for both wide and narrow-band excitations.