In this paper, we investigate the vibration characteristics of a Z-shaped beam with variable folding angles which is used to model a folding wing of a morphing aircraft under the condition of a fixed structure. The governing equations of motions for the Z-shaped beam are formulated. For a specific set of material and geometrical parameters, the first three in-plane and the first two out-of-plane linear frequencies of the Z-shaped beam are theoretically calculated, and validated by the experiments and numerical simulations. Additionally, the theoretical mode shapes at a fixed folding angle are compared to the experimental results and the finite element simulations. The theoretical results agree well with numerical simulations and experiments. The results obtained in this paper are helpful for designing and controlling Z-shaped beam structures, and can also be used as a basis to study the nonlinear dynamics of these structures.