The beloved pets, two of which have been cared for by their owners for more than 30 years, were taken in the early hours of Sunday,May 22.
Now the family is offering a reward for their safe return - no questions asked.
Louise, daughter of the tortoises’ owners, said: “My parents are absolutely devastated about their theft.
“The tortoises have been in the family for a long time and they are deeply missed.”
She added: “We are extremely concerned for their safety and welfare as they need to be in a specialised environment .
“Given the changeable British climate and they can be prone to respiratory and shell conditions if not given the correct care and diet.”
The creatures are two 2 Spur thighed tortoises both about 60 years old, one Horsfield tortoise and one Hermann tortoise about 13 year old.
The intruders forced entry through two locked gates to take the four pets.
The family is appealing for any information on the whereabouts of their pets, and have put up posters around town featuring pictures of the missing reptiles.
Anyone with any information should contact Bedfordshire Police on 101 quoting ref: JH/20324/2016.
Alternatively, anyone with information can also call 07905 088978, or email [email protected]