A multilayer film and a method of making the film are disclosed. In the method a multilayer film is post-oriented uniaxially in the machine direction resulting in a film that has a water vapor transmission rate of less than 2.5 g-mil/m2-day and an oxygen transmission rate of less than 1.5 cm2-mil/m2-day. The film of this invention is ideal for applications requiring low water vapor and oxygen transmission rates.