Open the Messages app
Find the conversation containing the text messages
Tap and hold the message you want to delete
Tap More
Select the message or messages you want to delete
Tap the trash icon
Tap Delete Message
To delete an entire conversation, swipe left on the conversation
Tap Delete
Confirm by tapping Delete again
To delete multiple conversations, tap Edit in Messages
Tap Select Messages
Select the conversations you want to delete
Tap Delete
Confirm by tapping Delete
To set messages to delete automatically, go to Settings
Tap Messages
Tap Keep Messages
Choose 30 Days or 1 Year
