The terminal phase, or Phase 3, of penetration is investigated using numerical simulations. Results of the first set of simulations, for zero-strength tungsten-alloy projectiles into armor steel at velocity of 1.5, 3.0, and 6.0 km/s are reported here. For these simulations, the mechanisms for Phase 3 penetration are limited to the transient deceleration of the eroding projectile and "afterflow," the extension of penetration after the projectile has fully eroded. It is found that for projectile L/D less than or equal to similar to2, there is effectively no steady-state penetration (Phase 2) and penetration is dominated by Phase 3. For projectiles of L/D greater than or equal to 3, steady-state penetration is achieved. For L/D greater than or equal to 3, the deceleration of both the nose and tail of the projectile are essentially independent of LID. For LID greater than or equal to 3, the target penetration associated with Phase 3 is found to increase with impact velocity approximately as P-3/D proportional to V (1.0). "After-flow" as a separate, identifiable mechanism could not be discerned in the results. We therefore question whether the phenomenon of "after-flow," as usually defined, exists; rather, projectile deceleration and crater depth growth are intimately coupled. (C) 2003 Elsevier Ltd. All rights reserved.