Analytic solutions are derived for a horizontal curved beam subjected to vertical and horizontal moving loads. The horizontal moving loads may be regarded as the centrifugal forces generated by vehicles moving along a curved path, which were rarely studied by previous researchers. Both a single moving load and a series of equidistant moving loads are considered. By superposition of the waves generated by consecutively moving loads on the curved beam, the conditions for the resonance and cancellation phenomena to occur are established. Compared with the numerical approaches, the present approach has the advantage that it provides clear physical insights into the various vehicle-induced phenomena on curved beams, while allowing us to identify the key parameters involved.