Hello, Which mail you are using? If its gmail See the Pic, Check the Box surrounded by Yellow circle in Your Gmail Account. and choose delete option .

See the Pics Attached

Check all of the email boxex (the small ones beside of the email titles) & select DELETE or DELETE all option, it will be somewhere nearer to the inbox's option...

Is this with one of hundreds of webmail services you use with a web browser like Firefox or is this with a email client like Mozilla Thunderbird?