Neck finishes suitable for containers formed of rigid materials are shaped to overcome problems which would otherwise occur if standard closures which perform satisfactorily with less rigid containers are used. One problem is that plugs (inner skirts) of closures are cut or shaved if they are oversize relative to the inner neck diameter. This problem is overcome by forming a chamfer or radius at the lead-in to the inside corner of the neck. A second problem ("ovality") occurs when the neck is not uniformly round; this problem is overcome by forming a cut-out section at the upper outer corner of the neck so that the maximum neck diameter engages the inside of the outer cap skirt below the top edge, thereby lessening outward distortion of the outer skirt.