Soft toys Woody Bear and Ronnie the Raccoon are familiar to thousands of families who visit Pleasurewood Hills in Lowestoft, Suffolk, every year.
They were removed from the park's gift shop at about 14:35 BST on Wednesday.
The characters were created specially for the park's opening in 1983 and carry "sentimental value", staff say.
A third stuffed mascot, Clarence the Cat, was left untouched.
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Pleasurewood Hills is one of the most popular attractions in the east of England with more than 200,000 visitors a year. The life-size Woody mascot is a familiar sight in the grounds.
Marketing manager Kate Wood said park staff were "absolutely distraught" to learn of the theft.
"We have managed to get the registration of the two male offenders who took Woody and Ronnie and the police have been informed," she added.
"Instead of pursuing the matter legally further however, we just want our characters back and would just ask for the safe return of the two characters back to the park, and no further action will be taken."
She confirmed that CCTV at the park was also being checked.
The mascots are the only ones in existence and created specially by soft toy makers Lefray for Pleasurewood Hills, which celebrates its 35th birthday next year.
Staff at a leisure park are appealing for the safe return of two beloved mascots that have been stolen from a display.