Pressure Relief Valve with High Pressure Opening and Closing Functionality

One-way pressure relief valves with structure providing high pressure opening and closing functionality are disclosed. Valves of the types described herein may be applied to a product package with flexible walls, for example a package containing dry roasted coffee, to allow gas to escape from the package while preventing entry of ambient air into the package. The valve structure provides a high-pressure valve which both opens and closes at high pressure internal to the package. The valve structure eliminates or reduces excessive expansion of the flexible-walled package caused by pressure increases within the package and eliminates or reduces excessive contraction or paneling of the flexible-walled package caused by increases in ambient pressure outside the package providing for an aesthetically improved package while also maintaining the quality of the packaged product.