Mounting assemblies can be used to retain an inflatable airbag cushion in a packaged configuration and attach the cushion to a vehicle structure. The mounting assemblies can have a mounting bracket and a wrapping member. The assemblies can also have a connecting member that connects the mounting bracket to the wrapper. The mounting bracket is attached to a vehicle structure and the wrapping member wraps and retains the cushion after it has been rolled and/or folded. During airbag deployment, the wrapping member releases the cushion so that it can be fully inflated and the mounting structure continues to anchor the cushion to the vehicle structure.