Yes, ammo can be stored for extended periods of time, but it is generally not recommended. A typical advisory: Long Term Ammunition Storage Made Easy
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The concern with the long term storage of ammunition storage is the corrosion on the shell casings. Corrosion comes from excessive moisture reacting with the brass casing or the primer making the round dangerous to fire. Nevertheless there are very easy ways to store your ammunition for a considerable amount of time and if you have a ammunition stock pile you are wanting to store there are a few things you need to think about. The key to successful storage is to remember: humidity is the enemy! You can easily store modern ammunition in paper boxes for several years inside your house, which typically has a controlled humidity level, without issue. I have even seen brass cased ammunition stored in cardboard boxes in a horse barn for one to two years (not that I would recommend it) without any noticeable corrosion on the casings. This does not address the challenges of storing ammunition for 3-5 years or longer.

It is important to note not to store you ammunition longer than necessary. Now, what do we mean by this? Rotate your ammunition whenever possible. So, instead of storing 5000 rounds of 5.56 or .223 for 10 years, mark each ammo can with the date you acquired the ammunition and the ammunition type. As you acquire more ammunition, of equivalent type, use the oldest ammunition first. This provides you a method of keeping your ammunition stock as fresh as possible

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