A critical hotspot is just large and hot enough that it can itself react, and go on to spread reaction into the cooler surrounding explosive, before it is cooled by heat conduction. This paper describes how previously-published hydrocode models were used to obtain critical hotspot criteria for HMX. The results compare well to those in the literature. In the simulations, which account for hydrodynamics, heat conduction and Arrhenius chemistry, reaction propagates outwards from hotspots via a flame driven by heat conduction. The flame propagation speed is compared to data for HMX from high-pressure diamond anvil cell experiments, leading to a new explanation for the negative pressure dependence sometimes observed in experiments.