A theoretical model for Density Wave Oscillations (DWOs) flow instability in parallel rectangular channels under periodic heaving motion is established with a lumped mathematical model based on homogenous hypothesis. The parallel rectangular channels comprise of the entrance section, the heating section, the riser section and the upper- and lower plenums, which guarantee the isobaric pressure drop condition between channels and the model consists of boiling channel model, pressure drop model, parallel channel model, additional pressure drop model generated by heaving motions, the constitutive and numerical models. The effect of periodic perturbation is introduced through additional pressure drop in the momentum equation. The model is validated with experimental data of a twin-rectangular-channel flow instability experiment under static condition. Then the flow instability in parallel-rectangular-channel system is studied under periodic perturbation and the margin of flow instability and the threshold power of the system under static condition is calculated as basis condition for comparison. The effect of the amplitude and period of perturbation is analyzed analytically and the results show that the amplitude and period of perturbation shows little effect on flow instability. While when the additional pressure difference introduced by heaving motion is comparable with that under static condition, the effect of amplitude becomes stronger. And the period of perturbation strongly effects the threshold power when it is identical to that of natural period of the system, which can be explained by resonance between the perturbation and the system. And this effect is even stronger when the asymmetric heating condition is introduced.