Neil Molloy disappeared on Thursday and officers say they want to find him as quickly as possible.
Mr Molloy was spotted boarding a number six bus at Forth Valley Royal Hospital, bound for Falkirk bus station, at around 1.45pm that day. It is thought he got off at Main Street, Bainsford, around 25 minutes later.
He is then believed to have been on Larbert Road, near Bonnybridge Golf Club, at around 5.50am on Friday.
Officers are carrying out inquiries in the local area in a bid to find him safe and well.
They are asking anyone who has seen him, or who can help with the investigation, to come forward.
Mr Molloy is described as 5ft 10in, with an average build and a local accent.
He wears silver-framed glasses and was last seen wearing grey trousers, a light grey jacket and a white shirt.
Inspector Adrian Wright, of Alloa police station, said: “We are keen to find Neil as quickly as possible and I’d urge anyone who has seen him or has information that can help us with our inquiries to please come forward immediately.”
Police can be contacted on the 101 number.