A frangible projectile for gun ammunition wherein the projectile includes a core 96 formed from one or more metal powders which are pressed into a self-supporting compact and incorporated into a metal jacket 10. The metal jacket is initially cup-shaped (generally cylindrical in overall geometry) with an open end 14 and a closed end 16. In accordance with one embodiment of the present invention the closed end of the jacket becomes the trailing end of the projectile. In another embodiment, the closed end of the jacket becomes the leading end of the projectile. In either embodiment, that surface 20 of the closed end 16 of the jacket which faces inwardly of the volume of the jacket is indented and stressed over substantially its entire area in accordance with a pattern of indentions 22 which enhances the frangibility of this closed end of the projectile when the projectile strikes a target. In either embodiment, upon the projectile of the present invention striking a relatively hard target, the initially closed end of the jacket, which now has been indented and stressed, disintegrates into minute particulates, each of which loses its momentum rapidly such that these particulates fall harmless away from the target.