You can either e-file Form 8868 or mail a paper copy to the IRS. The IRS recommends e-filing for faster processing and instant status updates. 

However, if you choose to file a paper copy, it must be mailed to the following address:
Department of the Treasury,
Internal Revenue Service Center,
Ogden, UT 84201-0045.

When filing an extension for Form 8870, the IRS only accepts paper-filing of Form 8868. In that case, the extension form must be sent in paper format to the address mentioned above.