Mark Calvert was last seen in south Bradford on May 27.
He is described as being about 5ft 10ins tall, of medium build and was last seen wearing a red jacket, black bottoms and black Adidas trainers.
A police spokesman said: "There are concerns for his welfare as he may be sleeping rough.
"He is also believed to have an injury from a motorbike collision which may need further treatment."
Anyone with information can contact police on 101, quoting log 1528 of 27 May, or use the live chat facility on the West Yorkshire Police website.