Tax March organisers say they have arranged demonstrations in more than 150 locations.
Mr Trump broke a long-held tradition by not releasing his paperwork during his presidential campaign.
His critics want to know who he has been dealing with and if there are any conflicts of interest.
"I think it is critical we know about his investments, his donations and any entanglements he has," said one protester, Chuck Wash, at a march in Washington DC.
There is no law requiring presidents to release their tax returns, but Mr Trump has found himself under public pressure and some information from a 2005 tax return was leaked to the media last month.
The protests were timed to coincide with the traditional mid-April deadline for Americans to file their tax returns.
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