The initiation of propagating detonation in PBX 9502 and PBX 9404 by jets of copper, aluminum, and water is numerically modeled using the two-dimensional Eulerian hydrodynamic code 2DE with the shock initiation of heterogeneous explosive burn model called Forest Fire. The Held experimental critical condition for propagating detonation is the jet velocity squared times the jet diameter. In PBX 9502, the jets initiate an overdriven detonation smaller than the critical diameter, which either fails or enlarges to greater than the critical diameter while the overdriven detonation decays to the C-J state. In PBX 9404 the jet initiates a detonation that propagates only if it is maintained by the jet for an interval sufficient to establish a stable curved detonation front.