Disclosed are polymer vials (110, 210) and injection stretch blow molding methods for making the same. A polymer vial has a base (112) having a base surface area and a sidewall (114) extending up from the base. The base and sidewall define an interior (116) configured to house product, the sidewall narrowing at an upper section of the vial to form a neck leading to an opening that provides access to the interior. The vial is optionally round and symmetrical about a central axis, a lower portion of the sidewall including a first surface that is outwardly curved along a first radius having an imaginary center positioned within the vial. The base is positioned below the first surface and is substantially flat such that at least 80% of the base surface area has a standing base surface occupying a single plane.