A unit dose package of a liquid nutritional product comprises a form-stable, cup shaped container with a capacity of less than 70 ml having a rim, a frustoconical sidewall and a base. A quantity of the nutritional product is enclosed within the container and a foil closure is sealed to the rim. The container is formed of a laminate comprising a barrier layer of highly 5 orientable EVOH having an ethylene content of less than 31 mol %, preferably around 27 mol %, and an oxygen transmission of less than 0.0068 ml/ml/year, between an inner carrier layer and an outer carrier layer. The package is especially adapted for long term storage of oxygen sensitive products.