A process for making a shrink pouch having strong shrink tension in the pouch transverse direction and minimal or no shrink tension in the pouch longitudinal direction is provided. The process includes the steps of reinflating and cold-stretch orienting a previously collapsed blown film and feeding the cold-stretch oriented blown film in a flattened configuration into a side-fed pouch making machine, whereupon the longitudinal direction of the blown film becomes the transverse direction of the pouches thus formed, and vice versa. A shrink pouch having strong transverse shrink tension and little or no longitudinal shrink tension is also provided.