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In large explosive and propellant charges, relatively low shock pressures on the order of 1–2 GPa impacting large volumes and lasting tens of microseconds can cause shock initiation of detonation. The pressure buildup process requires several centimeters of shock propagation before shock to detonation transition occurs. In this paper, experimentally measured run distances to detonation for lower input shock pressures are shown to be much longer than predicted by extrapolation of high shock pressure data. Run distance to detonation and embedded manganin gauge pressure histories are measured using large diameter charges of six octahydro-1,3,5,7–tetranitro-1,3,5,7-tetrazocine (HMX) based plastic bonded explosives (PBX’s): PBX 9404; LX-04; LX-07; LX-10; PBX 9501; and EDC37. The embedded gauge records show that the lower shock pressures create fewer and less energetic “hot spot” reaction sites, which consume the surrounding explosive particles at reduced reaction rates and cause longer distances to detonation. The experimental data is analyzed using the ignition and growth reactive flow model of shock initiation in solid explosives. Using minimum values of the degrees of compression required to ignite hot spot reactions, the previously determined high shock pressure ignition and growth model parameters for the six explosives accurately simulate the much longer run distances to detonation and much slower growths of pressure behind the shock fronts measured during the shock initiation of HMX PBX’s at several low shock pressures.