Officer are appealing for information about Philip Adamson, who has been reported missing from his home in Bingley.
The 38-year-old was last seen at his home at around 5.45am on Monday.
He was last seen wearing dark blue work trousers, a dark blue work shirt and white shoes.
Detective Inspector Sally Shipley, of Bradford District CID, said: “Philip has now been missing for two days and concerns are growing for his welfare as his disappearance is out of character.
“We have carried out enquiries across Bradford District and will be returning to the Bingley area today to make further searches.
“He is thought to be on foot and it is possible that he may still be in the local area.”