Aspects of the disclosure relate to airbag systems for vehicles. The airbag systems may reduce the secondary impact forces felt by an object upon rebounding from an initial impact with an external airbag by encasing or substantially surrounding the pedestrian with the external airbag. The airbag system may include an initial impact airbag and a secondary impact airbag, wherein the secondary impact airbag is configured to reduce injury caused by a secondary impact of an object upon after an initial impact of the object with the initial impact airbag. The initial impact airbag may be configured to be deployed at a location where the object is predicted to collide with the vehicle. The secondary impact airbag may comprise one or more arms configured to surround the object upon the initial impact.