The focus in this paper is on investigating the influence of hinge friction on the steady-state dynamic response of a transversally base-excited shallow arch. Two semi-analytical models are derived by applying an assumed-modes approach based on sinusoidal modes and Craig–Bampton modes respectively. It is shown that both models give qualitatively and also to a great extent quantitatively similar response results. Hinge friction induces the presence of equilibrium sets rather than static equilibria. Furthermore, the influence of friction on the load-path for a quasi-static acceleration loading is illustrated. In the steady-state analysis of the semi-analytical models, amplitude–frequency diagrams are presented. These plots are obtained by solving two-point boundary value problems in combination with a path-following technique. Local stability and bifurcation analysis of periodic solutions is carried out using Floquet theory for systems of Filippov type. Especially for low excitation amplitudes, the responses dramatically change due to hinge friction, since these responses are dominated by hinge stick. Near resonances and in the case of high-amplitude excitation, the frictional hinge will only slip and the influence of hinge friction is significantly reduced. When hinge friction is relevant, the Craig–Bampton model is expected to predict responses more accurately.