Apps like Backup Everything and MyBackup Pro claim to be able to. What have you already tried? I have never tested these apps for that purpose, so I can't say it will do exactly what you want. You'll have to try it out and see. I know most of the strictly SMS backup apps out there won't do it.

 

SMS Backup will back them up to your gmail account.

Download SMS Backup + for your Android phone on AppBrain

 

I thought Mms pics were saved to the sd card automatically. ...I don't thing sms backup backs up the pics...but I have only used it for backing up the sms.

 

MyBackup Pro didn't restore the MMS on my Droid... It was on the main reasons I purchased the app. Titanium Backup didn't either.

Edit: MyBackup Pro did restore my MMS, but only from the first backup I did. I tried on the later backups, and they failed.

This app is only for SMS messages, not MMS...

 

https://market.android.com/
I did a search for mms backup and came up with the following on the first two pages. these were the ones that look like they can handle it.




https://market.android.com/details?id=net.cpedia.backup2gmail&feature=search_result

https://market.android.com/details?id=com.zegoggles.smssync&feature=search_result

https://market.android.com/details?id=com.brilaps.android.txtractpro.withmms&feature=search_result

https://market.android.com/details?id=com.BackupEverything&feature=search_result

https://market.android.com/details?id=com.brilaps.android.txtract.lite&feature=search_result

https://market.android.com/details?id=com.Backupapp&feature=search_result

https://market.android.com/details?id=com.xmobileapp.xarchive&feature=search_result

 

I was seeking for this same thing. Thanks for the last post, I tested Backup to Gmail. and it works. This application creates another label called MMS for them, and the pictures are shown as attachments. Title and content text of the MMS is also present. I think it's what you are looking for as it is what I am.