Based on the Fourier and Fourier sequence transforms, and the transfer matrix method, the resonance of a periodically elastically supported continuous beam produced by a series of moving loads and its cancellation effects were investigated. By using the Fourier and Fourier sequence transforms, the dynamic response produced by single moving loads was represented by the integral of the response function over the representative span. The response function and eigenvalue equation of the periodically elastically supported continuous beam were obtained using the transfer matrices between the beam and its elastic supporting points. According to the superposition principle and the expression of the dynamic response of the beam under single moving loads, the dynamic response of the beam under a series of equidistant moving loads was obtained. Using the frequency domain dynamic response of the beam under single moving loads, the resonance and cancellation conditions of the periodically elastically supported continuous beam subject to a series of equidistant moving loads were established. Numerical results show that, when the loading velocity and distance satisfy the resonance condition, resonance will occur; when the condition for resonance cancellation is fulfilled, the effect of resonance cancellation will occur.