There is usually a certain camber in cable-stayed bridge to meet the needs of drainage. Considering the initial configuration and support stiffness of cable-stayed bridge, the multi-cable-stayed shallow-arch model with vertical elastic constraints is established. Firstly, based on the classical dynamic equations of cable and shallow arch, the theory of in-plane free vibration of the model is deduced by dividing the shallow arch into several segments at the cable-arch coupling point. Then, taking the double-cable-stayed shallow-arch model as an example, the in-plane eigenproblem is solved by separation-of-variable method. At the same time, the corresponding ANSYS model is established, and the frequencies and mode shapes calculated by the present method are compared with the results of ANSYS, which verifies the correctness of the method and model in this paper. Finally, the parametric analysis of the dynamic properties of the model is conducted systematically. The results show that the vertical stiffness has a significant effect on the dynamic properties of the system.