This is one of those things where is not a law that says "you may not keep cash in a SD box," however there are several laws and regulations that make it sub-optimal or difficult to disprove an allegation that you broke some other law.
1. No FDIC insurance (no legal impact obviously but flooding is not unheard of)
2. If you have a large amount of cash with no traceable origin, the IRS is definitely going to want to know how you came about it. Concealing the source of cash violates federal regulations.
3. I've heard many times that directly taking cash out of circulation is itself a crime, and that courts have interpreted SD boxes as such, however the only actual source I can find says that physically destroying cash (e.g. burning it) is a crime.
I have edited my post to reflect the fact that I'm actually not 100% sure now :)
That comment worried me: I found this reference from BankRate saying putting cash in a safety deposit box is only illegal if it is concealed for tax evasion purposes.
I can't seem to find anything definitive that identifies the legal grounds to claim that the storage of cash in a safety deposit box is illegal in the United States, but I did come across a couple of references that indicated that certain banks have included the prohibition in their terms of use.
Given that the contents of a safe deposit boxes are not covered by FDIC insurance, I can see why it's not necessarily recommended.
