Book excerpt: The initiation of propagating detonation in PBS 9404, PBX 9502, and X0219 by hemispheric intiators of PBX 9404, 1.8 g/cm3-TATB, and X0351 is described numerically, using the two-dimensional Lagrangian code, 2DL, and the Forest Fire rate to describe the heterogeneous explosive shock initiation process. The initiation of propagating detonation in the insensitive explosive PBX 9502 by triple-shock-wave interaction from three initiators has been modeled using the three-dimensional, reactive, Eulerian hydrodynamicd code, 3DE.