New iPhone 11 won't turn off

In addition to the correct advice Tesserax provided, you might want to Force Restart your phone by doing the following (follow these directions precisely).

• Press and quickly release the volume up button
• Then immediately press and quickly release the volume down button
• Then immediately press and KEEP HOLDING the side power button (keep holding it past the swipe to power off and even when the screen goes completely black) until the Apple Logo appears - THEN let go

Step 1: Press and hold the Side button and either the Volume Up or Down button until the 'Slide to Power Off' option appears on the screen.

Step 2: Now simply perform the 'Swipe to Power Off' operation and wait for the iPhone to shut down.

If this doesn't work, try using Siri to turn off the phone.

If that doesn't work either, there may be something amiss with this phone. If you purchased it new within the last 14 days, you have the option to return it for either a refund or a replacement. Otherwise, I suggest you contact Apple Support directly for further assistance with this matter. You can do so simply by selecting the "Get Support" link in the upper right-hand side of this forum's web page.