Abstract We study how the influence of the shock wave appears in neutrino oscillations and the neutrino spectrum using density profile of adiabatic explosion model of a core-collapse supernova which is calculated in an implicit Lagrangian code for general relativistic spherical hydrodynamics. We calculate expected event rates of neutrino detection at Super-Kamiokande and SNO for various θ$_{13}$ values and both normal and inverted hierarchies. The predicted event rates of ¯ ν$_{e}$ and ν$_{e}$ depend on the mixing angle θ$_{13}$ for the inverted and normal mass hierarchies, respectively, and the influence of the shock wave appears for about 2 - 8 s when sin $^{2}$2 θ$_{13}$ is larger than 10 − $^{3}$. These neutrino signals for the shock wave propagation is decreased by ≲ 30% for ¯ ν$_{e}$ in inverted hierarchy (SK) or by ≲ 15% for ν$_{e}$ in normal hierarchy (SNO) compared with the case without shock. The obtained ratio of the total event for high-energy neutrinos (20 MeV ≦ E$_{ν}$ ≦ 60 MeV) to low-energy neutrinos (5 MeV ≲ E$_{ν}$ ≦ 20 MeV) is consistent with the previous studies in schematic semi-analytic or other hydrodynamic models of the shock propagation. The time dependence of the calculated ratio of the event rates of high-energy neutrinos to the event rates of low-energy neutrinos is a very useful observable which is sensitive to θ$_{13}$ and mass hierarchies. Namely, time-dependent ratio shows clearer signal of the shock wave propagation that exhibits remarkable decrease by at most factor ∼ 2 for ¯ ν$_{e}$ in inverted hierarchy (SK), whereas it exhibits smaller change by ∼ 10% for ν$_{e}$ in normal hierarchy (SNO). Observing time-dependent high-energy to low-energy ratio of the neutrino events thus would provide a piece of very useful information to constrain θ$_{13}$ and mass hierarchy, and eventually help understanding the propagation how the shock wave propagates inside the star. PACS numbers: Valid PACS appear here 2 ∗ The University of Tokyo; Electronic address: shiok@iis.u-tokyo.ac.jp