How do I open the back of a S4 Samsung galaxay cell phone

Samsung Galaxy S4: How to open back battery cover:

1) Flip the phone over so you see the back cover..
2) Locate the notch on the side of the phone with your fingernail and pull the cover easily up to unlatch that area and all areas around the phone.. With one hard pull you can easily take off the whole cover.. don't be shy, your Samsung phone is sturdy enough to handle it.

All the blue arrows in the below image shows where the cover clicks into the inside of the phone to keep it closed.
3.) when you need to put the cover back on the phone.. place the cover over the back part of the phone, noting that the camera hole in the cover goes at the top..

Then grip your left hand on the left side of the phone and your right hand on the right side of the phone.. apply pressure to each side to click the latches to the phone locking it in place.

Afterwards, run your fingers along the back sides of the phone to see if there are any bulges (a latch may not have clicked in place). Either apply pressure there to click it into place or you may have to take the cover off again and try again.

It's very simple and easy once you get the hang of it.

How to Open Samsung Galaxy S4 Back Cover Insert Battery SIM Replace Back...

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Bending the back cover will not damage it because it is plastic.. unless you bend it to crease it. Below is Samsung's durability test.
https://www.youtube.com/watch?v=UrhCz6PnT78
(you may need to copy and paste this link to make it work)
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1. Flip it over on it's back
2. You will find a groove on the left side of the mobile
3. Use ur nail or anything thin to insert it into this groove
4. Start pulling upwards and you will find yourself able to open the cover.
Here's the link to help you out

How to Open Samsung Galaxy S4 Back Cover - Insert ...

Take a look at iFixIt, they have lots of repair guides for mobile devices. Here they are the S4. Samsung Galaxy S4 Repair