A bullet comprised of a jacket of malleable metal having a closed nose portion and a rear end portion defined by a cylindrical wall, the closed nose portion having wall-weakening areas encapsulating a forward core made of a deformable material which promptly deforms, collapses axially, and expands radially to a substantial extent along with the weakened wall areas, when the bullet strikes a target. The nose portion has wall-weakened areas which are ruptured by the core material to produce a collapsing and radially expanding action. These weakened wall areas are in the form of longitudinally extending, deep, internal or external, circumferentially spaced grooves with underlying web areas which are ruptured by the core material, to produce the collapsing and expanding action. This core is preferably made of rubber, urethane, silicone, or one of a substantial number of plastics, each of which has a hardness within a range of Shore A 20 to Rockwell 122. A second core, made primarily of metal or plastic, and preferably softer than the metal of the jacket, is seated, under pressure, behind the nose core and within the rear end portion of the jacket. The advantages of the bullet result from the fact that it collapses axially and expands widely and quickly, upon striking the target, and yet penetrates an adequate distance, without losing an appreciable amount of weight, and without passing through the entire body of the target, to thereby provide an adequate penetration, optimum expansion bullet.