Shane Donnelly, who may also be known by the surname Barr, was involved in a two-vehicle crash on the A7 near the Lindean junction, north of Selkirk in the Borders, on Tuesday night.
Emergency services attended the incident at around 7.10pm, but Mr Donnelly, who is believed to have been one of the drivers, was not at the scene.
He is described as being 6ft, with brown hair, facial hair, and blue eyes.
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The woman driving the other car involved was taken to Borders General Hospital by ambulance for treatment.
Inspector David Aitchison said: “We are concerned for Shane’s welfare as we believe he may have suffered injuries, and it is imperative that we trace him as soon as possible.
“Significant resources, including the police helicopter and dog branch, have been involved in searches of the local area and inquiries are continuing.
“Shane has links across the Scottish Borders and I am keen to hear from anyone who may have information about Shane’s whereabouts. Please get in touch, as we need to ensure his safety.
“I am also appealing directly to Shane, if you are reading this, please let us know you are safe and well.”
Anyone with any information is asked to call 101, quoting reference 3784 of January 14.