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To be snowed under (with something)

 
Examples:

"I'm sorry I didn't come to the meeting, but I was snowed under with work."

"I'm sorry I haven't replied to your email before now,
but I've been snowed under with paperwork."

"I'm afraid I can't come to the cinema this evening.
I'm snowed under with work and I have to try to finish it today.
I'll probably be here until late evening."

 
Use:

To be snowed under (with something) means that you have so much
to do that you cannot do anything else. The first thing to do is to try to clear the "snow".

This idiom is often used when we apologise for not being able to do something/meet someone.

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