The pressure and flame temperature dependences of mass burning rates for hydrogen mixtures are studied experimentally and numerically. Flame speeds and mass burning rates were extracted from outwardly propagating flames for equivalence ratios from 0.85 to 2.5, pressures from 1 to 25 atm and flame temperatures of 1500 to 1800K. At low pressures, the mass burning rate is experimentally observed to increase with pressure, while at greater pressures, the mass burning rate is found to decrease with pressure for both lean and rich conditions. Negative pressure dependence of the mass burning rate is observed at lower pressures for mixtures with lower flame temperatures. Additionally, the temperature dependence of the burning rate increases substantially with pressure-indicative of a higher global activation energy and Zeldovich number. At lower pressures, predictions using recently published chemical kinetic models agree reasonably well with one another and the experimental data. However, at higher pressures, the predicted mass burning rates differ substantially from model to model and with experimental data. Much larger disparities are apparent among model predictions themselves at fuel rich conditions. Variations of nearly a factor of two in predicted burning rates are noted. Numerical studies on the effect of pressure on species and flux profiles and sensitivities to elementary rates were conducted for a lean and a rich mixture with flame temperature near 1600K. Flux analyses revealed that there is increased flux of the H radical through H+O2(+M)=HO2(+M) at higher pressures, leading to increased flux through two competing channels HO2+H=H 2+O2 and HO2+H=OH+OH and significant influence on the critical branching factor. Mole fractions of all radical species (except H2O2) are lower at higher pressures, and the fraction of the radical pool composed of HO2 is increased. As the pressure is increased, the extended second explosion limit is shifted to higher temperatures. Consequently, the portion of the flame zone that exhibits explosive chain branching is restricted to a narrower, higher temperature window - indicated by the shift of the peak for all radical species and reaction fluxes to higher temperatures. The sensitivities of mass burning rates to several elementary rates increases considerably with pressure. The temperature window of peak sensitivity to rates moves to a narrower, higher temperature range with increasing pressure, most noticeably for reactions of HO2 with H and OH. Given that reactions of HO2 with H and OH have relatively large uncertainties in their rates and temperature dependences especially above 1000K, it appears likely that these reactions are largely responsible for the disagreement among the models and experimental data.