We have measured the reaction propagation rate (RPR), or deflagration rate, in octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) powder in a diamond anvil cell over the pressure range 0.7-35 GPa. Numerical simulations of the RPR of pressurized HMX were also performed for comparison to the experimental results obtained. The simulated RPR values closely approximate the observed rates at pressures up to 3 GPa, and serve as a bridge to lower-pressure deflagration rates for HMX in the literature. However, at higher pressures the simulated RPR values deviate significantly from our experimental results. This suggests that further refinement to the computational model is required for the calculated RPR values to approach those observed at higher pressures.