The group conducted simultaneous raids on the five-star Angsana Phuket Resort at Laguna Phuket, the Big Buddha ATV camp and a souvenir market south of Phuket City.
The DNA of the three baby elephants is to be checked amid concerns that the baby elephants may have wrongly been separated from their mothers in other parts of Thailand.
A number of snakes were also seized from a snake show at the Phu Thai Souvenir Market. Twenty-one protected Thai snakes were taken and will be released into the wild on Phuket by authorities.
Background checks are being made on another 20 imported snakes.
At the Angsana Phuket Resort - which was the Sheraton Grande Laguna Phuket Resort until it was renovated and relaunched last year - investigators found two baby elephants when they expected to find one.
The resort's GM told Phuketwan last year that Laguna Phuket had taken over management of the elephants that entertain tourists there to ensure they were properly cared for at all times.
The raids today were led by Federal Bureau of Investigation Deputy Chief Sriwara Rangsipramkul.
It is believed the FBI became involved following the suspicious deaths of adult elephants in a national park and concerns that body parts may have been taken for consumption.
Checks on Phuket have so far failed to sustain claims that elephant parts have been smuggled to Phuket to be eaten by fans of exotic food.
The more likely theory was also put that baby elephants are being taken illegally from national parks, but the provenance of the three baby elephants that were the targets of today's raids on Phuket has yet to be thoroughly checked.
The elephants in question are Popeye, Johnny, and a third as-yet unnamed youngster.