Employing the external force method to regard seismic impact and the three-region methodology to analyze the supercritical heated channel, a non-linear dynamic model was developed to investigate the transient characteristics of single channel or parallel channels under the impacts of vertical sinusoidal and seismic accelerations. The present model was validated against the experimental data, which could suitably estimate the additional pressure drop caused by the vertical vibrations. The influences of parameters on the seismic-induced oscillation conducted in a supercritical heated channel indicated that a longer heated length, uprating operation power and a larger outlet loss coefficient all exhibit unstable effects, while the increase of inlet loss coefficient, a larger tube diameter and a lower inlet fluid temperature would tend to stabilize the system. Moreover, the supercritical fluid would present a high natural frequency in the very small NP-SUB region. The parametric effects on the parallel channel system are related to the inherent stability nature of initial state and the interactions among channels. The more uneven heat flux distribution among channels would cause a larger vibration-induced oscillation. In particular, when it is combined with the resonance effect, the system may exhibit much larger oscillations than in the case of non-resonance.