In order to shed some light on the response of explosives to the attack of smalldiameter projectiles such as shaped charge jets, we conducted a computational study using the 2DE code and the Forest Fire explosive initiation model. Simulations of copper-jet attack against Composition B were made in order to determine modes of initiation and critical velocity for initiation as a function of jet diameter. We modeled the jet as a nonstretching cylindrical projectile with a flat tip. Its diameter was varied between 0.3 mm and 12.0 mm and its velocity was varied between 0.8 km/s and 15.0 km/s. We observed two modes of initiation: (1) prompt, impact-mode initiation for both subsonic and supersonic penetration and (2) delayed, penewation-mode initiation only for supersonic penetration by small-diameter jets. The velocity threshold for large subsonic jets agrees with the Jacob-Roslund formula. For jets with diameters smaller than the failure diameter of the explosive they attack, higher velocities than predicted by Jacobs-Roslund are required for initiation. A critical threshold between impactand penetration-mode initiation was determined over the entire supersonic range. A similar threshold between penetration-mode initiation and initiation failure has not yet been determined due to limitations of the code.