The flame structures and extinction characteristics of undiluted hydrogen-oxygen strained diffusion flames at high pressures with detailed and reduced chemistry are numerically studied with an intention of application to acoustic instabilities of rocket engines. The numerical results of extinction strain rate for undiluted hydrogen-oxygen flames are found to be qualitatively different from those for hydrogen-air flames in that extinction strain rate for undiluted hydrogen-oxygen flames increases linearly with pressure up to 100 arm whereas extinction strain rate for hydrogen-air flames saturates around 50 atm. Comparison of the characteristic flow rime with the characteristic chemical time shows that extinction strain rate varies linearly with pressure for flames controlled by two-body chain-branching reactions that are found to be dominant up to 100 atm. The four-, three-, and two-step reduced mechanisms are also tested to exhibit that the linearity of the extinction strain rate with pressure is preserved. Based on these results, the asymptotic methods, previously used in low-pressure hydrogen-air flames, can be extended to predict the asymptotic structure of hydrogen-oxygen flames at high pressures. On the other hand, the fall-off effect and real-gas effect are found to be minimal on extinction characteristics. Since the characteristic flow time is estimated to be several orders of magnitude shorter than the characteristic acoustic time in rocket engines, acoustic responses are satisfactorily reproduced from the quasisteady flame structures. Finally, the sensitivity analysis identifies the reaction step, H + O-2 + M --> HO2 + M as a favorable reaction path to stabilize acoustic oscillations by depressing the reaction rare.