A forwardly concave insert for a hollow charge of an armor-piercing missile or projectile has an inner peripheral wall with linear generatrices and an outer peripheral wall with at least partly curved generatrices diverging from the inner wall surface to an annular zone of maximum wall thickness at more than half the distance from the point of the cone to its base, the outer generatrices having centers of curvature lying beyond the cone axis on radii which are perpendicular to the inner wall surface at that annular zone. The arcuately curved sections of these outer generatrices merge tangentially into substantially straight-line sections converging at the cone axis into the aforementioned point.