According to the mechanical characteristics of cable-stayed bridge and based on the classical dynamic theories of cable and shallow arch as well as the dynamic equilibrium conditions at the joint between them, the in-plane free vibration theory of a cable-stayed bridge was established. Simultaneously, the geometric nonlinearity of shallow arch and cables were considered in the model in order to account for the effects of both deck’s camber and cable’s sag in the practical long-span cable-stayed bridges. First, the shallow arch was divided into several parts according to the coupled joints of cables and deck. Based on this point and using the Hamilton principle, the in-plane free vibration equations and boundary conditions of multiple cable-stayed shallow-arch system were derived. Then, applying the method of separation of variables, the linearized equations and boundary conditions governing the in-plane free vibration of the system were established. Next, taking the double-cable-stayed shallow-arch as an example, the in-plane eigenvalue problem was solved using the proposed theory and method in this paper. At the same time, a finite element model of the double-cable-stayed shallow-arch was established to verify the analytical solutions, and consistent results were obtained. Finally, the analysis of some key parameters of the CFRP bridges was conducted. It can be found that modulating the rise of arch in a certain range can only affect a modal frequency of the system, while others are rarely influenced. The results show that CFRP cables can improve fundamental dynamic properties of the system, i.e., the bridge with CFRP cables can overcome the deterioration caused by stress relaxation of cables. The content of the paper focuses on the in-plane free vibration of multiple cable-stayed shallow-arch system and enriches the study of the mechanical properties of cable-stayed bridge, which can be used to guide the design of this kind of bridge in practice.