According to court documents, the account holders are accused of concealing their income or assets in order to pay less tax in the US.
These are the first cases to be brought against clients of the Swiss bank since it and the US government reached a deal to disclose the names of some customers who were suspected of acting illegally.
Details of the agreement are due to be announced this week and it has been suggested that the move marks the end of the confidential Swiss bank account, with Reuters reporting that the number of cases will "mushroom" in the near future.
Speaking to the Associated Press after the deal was agreed last week, Florida-based tax lawyer William Sharp said that it is unlikely the move would have gone ahead without UBS agreeing to hand over a "substantial" amount of information.
He predicted that "at least several hundred" names will have been given to the US authorities.
Written by Tony Aynsley