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Open Messages app and you will find all your messages there. Two methods :
1 - Tap and hold down any message and it will select that message. You can now select the messages you would like to delete (checkmark them). Then tap Delete button. If you don't see Delete button, tap the Options button and tap Delete.
2 - In Messages, tap the menu button (three dots at upper right). Tap Delete. Select the messages and tap Done/Delete.
If you have any questions or would like any additional information, please don't hesitate to ask.
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As you probably already know, when you delete something from your phone, only the reference to that file is being deleted and the actual files can be still recovered using third party data recovery applications.
The best option to make the deleted files/texts unrecoverable is, factory reset or completely erase the phone using a third party PC utility application like Android Data Eraser. Get it from here--> http://www.androiddataeraser.com/
You can also factory reset the phone two or three times after encrypting it to remove everything from the memory. Factory reset after encrypting will make the recovery application hard or impossible to recover them. Remember, factory reset without encrypting will not help. See here : http://www.cnet.com/how-to/the-best-way-to-completely-wipe-your-android-device/
There is also an android application that can be used to erase the deleted data (free space) from the phone. See here : https://www.protectstar.com/en/products/ishredder-android
I suggest you to do all these three steps and trust me, no application can recover anything from your phone.
If you don't want to factory reset your phone, then use iShredder app. But If you really want to make them totally unrecoverable, factory reset after encrypting and the first option are the best methods.
Although iShredder will overwrite the deleted data with null values to make them unrecoverable, we will not know how effective it will be. So I still recommend the first two methods along with iShredder.