The drivers stopped work about 10pm, claiming they had not been paid and were owed millions of baht by the Glenn Marine Group, which provides services when US warships are in South East Asian ports.
The nuclear-powered aircraft carrier USS Nimitz and an accompanying vessel, the USS Princeton, anchored off Phuket's east coast deep sea port yesterday.
A shuttle bus service has been running across the 20 kilometres between the deep sea port, at Ao Makham on Phuket's east coast, and Patong, the nightlife capital on Phuket's holiday west coast.
''It's a stand-off at the moment,'' a source told Phuketwan. just before midnight. ''The drivers say they haven't been paid and the Glenn Marine people say they have.''
About 350 peole were standing about, many appearing to be mildly intoxicated, the source said.
The military personnel, due back on board their ships, milled around in Patong after 11pm awaiting instructions from officers.
The designated drop-off and pick-up point is near the Patong Resort Hotel. Hotel staff said tonight they were aware of the issue and that the military personnel - in civilian clothes - had been milling about for several hours.
Most Americans are hesitant to use the alternative means of transport, Phuket tuk-tuks and taxis, because cabs on Phuket charge fares that are between six and 10 times higher than those charged in other parts of Thailand.
It is believed senior staff from both vessels were attending a function in Patong held by the Phuket Navy League to mark the ships' arrival.
The visit to Phuket by the Nimitz and the Princeton is due to last three days.