For free iPhone SMS backup you have great option of Apple iTunes. That is the free utility provided by Apple to transfer iPhone files like SMS, contacts etc. By this way you would have to sync iPhone data to PC. to run this process iTunes helps you.
If iTunes fails to transfer iPhone SMS then you can use third party File transfer iPhone tool. Interactive interface of this tool easily guides you to transfer iPhone SMS easily.
Step1. Connect your iPhone to PC.
Step2. Install File transfer tool on system.
Step3. Run application and select sms that you want to backup.
Step4. Click OK button and you SMS sent into system.
One can easily perform these interactive steps and transfer iPhone SMS.