I have an alternate solution. You can now go to the Dollar Tree and get 2.5 gallon zip lock bags. You get 5 in each box. Your magazines would fit in there and you can then pack as many as you can inside each one.
I have never heard of a plastic bag that would hold that many magazines and not break. But, the zippered ones that linen and bedspreads come in would be a good alternative.
Here is another idea. If these are not collectibles you need to keep for their value, why not tear out what you want and recycle the rest. You can also scan what you want and recycle the magazines to a retirement community or to the recycle center. Just some food for thought.