go to Inbox or Outbox or Sent - it doesn't matter because this methods delets all messages

Select Read on any message

Select Options

You will see Forward, Details, Delete, Use number, Use address and Delete all

Select Delete all

It will ask if you really want to delete all

You can press Yes at this point

All your message will be deleted

Gone for ever

One user posted that there's a way to group delete text messages in Settings, can you check that out? You can delete messages 1 by 1; go to Messages > choose a message > press options > Delete.