a strip of container carrier stock formed from a thin resilient plastic sheet material which is designed to be applied to containers by machines and which may particularly accommodate stretching forces applied nonsymmetrically relative to either the longitudinal axis of the stock or to the lateral axis extending across each laterally aligned series of bands . the stock of this invention is thus configured to be nonsymmetrical about the longitudinal axis of the stock or about a lateral axis extending through the midpoints of each row of container receiving aperture creating bands .