Supercritical water reactor (SCWR), a possible generation IV nuclear reactor, is expected to be more efficient and economical than the existing reactors. However, the possibility of thermal-hydraulic (TH) instabilities poses a challenge to its development. A generic pressure vessel (PV) SCWR concept, similar to the US SCWR design, is investigated at present for density wave oscillations (DWOs). An existing TH model, which was used earlier for the single-channel analysis, is extended here for the analysis of parallel channels. The TH model accounts for the regional heterogeneity in power distribution. The TH model is validated with the existing numerical results to access its capability to simulate the parallel-channel density wave instabilities (DWIs) in a supercritical water (SCW) system. Then, the TH model is used to capture the core-wide as well as regional modes of parallel-channel DWIs in the PV SCWR. The marginal stability thresholds are obtained for both the modes of DWOs and are compared. Subsequently, the aforementioned stability thresholds are compared with those obtained from the single-channel model as well, with the purpose to quantify the difference in stability thresholds obtained from the single-and parallel-channel analysis.