A modified flexible package includes a front elastomeric wall and a rear elastomeric wall. The front wall and the rear wall are sealed together at a top seal at a top end of the side walls. The top seal is formed by applying heat and/or pressure for a given dwell period, and is preferably a de-laminating seal. A first zipper part is attached to an inside surface of the front wall and has a first engagement member facing the rear wall. A second zipper part is attached to an inside surface of the rear wall and has a second engagement member facing the front wall. The first and second engagement members are engaged together. Both the top seal and the zipper engagement members are "pinch-grip opened" under a pinch-grip pulling force applied to the front and rear walls below the zipper. The front and rear walls have a strength sufficient to resist tearing and deformation under the application of the pinch-grip pulling force during pinch-grip opening. The invention provides a re-closable package that can be opened in an easy one-step manner--"pinch grip opening"--without an additional step of cutting, tearing or the like.