Abstract This study introduces a novel scheme for the discrete high-frequency forced vibration analysis based on discrete singular convolution (DSC) and mode superposition (MS) approaches. The accuracy of the DSC–MS is validated for thin beams and plates by comparing with available analytical solutions. The performance of the DSC–MS is evaluated by predicting spatial distribution and discrete frequency spectra of the vibration response of thin plates with two different boundary conditions. The frequency spectra of the time-harmonic excitation forces are in the form of ideal and band-limited white noise so that the natural modes in the frequency band are provoked. The solution exposes high-frequency response behaviour definitely. Therefore, it is hoped with this paper to contribute the studies on the treatment of uncertainties in the high-frequency design applications.