Robert Mee, 54, left his home in Lewes Gardens, Werrington, at about 9am where it is believed he had planned to get the bus to Bourne before returning home in the afternoon.
DS Shishminder Thind said: "We now know Robert didn’t go to Bourne as planned but instead got on a bus to Stamford.
"He got off the bus in Red Lion Square at about 9.40am on Monday and went to 'Today’s Local' shop. The last confirmed sighting we have of him is at about 9.50am heading passed Scotgate. From this point we do not know where Robert went, or if he is okay.
"I am urging anyone who may have seen Robert to get in touch with us as a matter of urgency to help us find him and make sure he is safe and well."
He is described as white, 5'10", with light brown hair which is balding, and wears glasses. It is believed he would have been wearing a red jacket, a baseball cap and a large black and red rucksack when he left home.
Anybody with information about Robert’s whereabouts should call us on 101 quoting incident 433 of September 7.
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