The Swiss Vapeur Park said in a statement online that "the offenders have forced open the doors of two different depots, and took the two trains".
One is a petrol-run train called BVB, while another is a steam train that runs on gas, said the park located at Le Bouveret.
"We do not understand how they have managed to load these trains, knowing that the BVB train alone weighs about 800 kilogrammes," it added.
The park said that its employees are "very affected by the theft" and appealed for anyone with information to contact police.
The value of the trains could not be quantified, said the park, "because these models were manufactured by volunteers who are passionate about mechanics".
"What has been stolen is thousands of hours of work," it added.