Abstract: The theoretical solution for the vibration of simply-supported beams under moving load series is derived. Based on the solution, the train speeds inducing resonance and two types of cancellation for simply-supported beams are obtained, and the occurrence mechanisms of resonance and vibration cancellation phenomena are clarified. It is demonstrated that there are two types of vibration cancellation effect for simply-supported beams under moving load series: the first cancellation related to a single load behavior, and the second related to the distances between moving forces. When cancellation occurs, the free vibrations after the moving loads depart from the bridge are counterbalanced to null, thus the bridge response becomes smaller. The condition of cancellation is more decisive than that of resonance. When the train speeds meet conditions of both phenomena, cancellation plays a predominant role, and resonance disappearance can be expected. Theoretically, the phenomenon of resonance can be avoided by adjusting the length ratio between a vehicle and a bridge. The dynamic responses of two simply-supported beams are analyzed in the case study, which verify the validity of the theoretical analysis.