Most of the existing analytical solutions to the vibration of cable networks interconnected by cross-ties are developed based on string theory, where the effect of cable bending rigidity on cable vibration is ignored. However, the bending rigidity of cables strongly influences the natural frequencies and vibration mode shapes of short and stout cables and long cables at higher modes. Hence, this paper considers cable bending rigidity to form a closed-form solution that can be used in determining the natural frequencies and mode shapes of cable networks. The analytical solution of the cable network model with hinged-end boundary conditions is derived. It can be combined with other existing techniques to analyze the dynamic behaviors of a two-cable network with partly fixed supports. The analytical solution derived from this paper can be degenerated to the same solution without considering the cable bending rigidity in previous studies. The accuracy of this analytical solution considering cable bending rigidity is verified by finite element analysis. The effects of bending rigidity on the vibration frequencies and modes of the cable network with inclined and flexible cross-link are investigated in detail. This analytical solution can be applied to backward analysis to identify the cable tension of a two-cable network with partly fixed supports.