Hi Dan,
Thanks for your question!
Whenever your pet’s behavior changes, it could be an indicator of a health problem. This type of behavior (showing interest in licking or eating non-food items) is called “pica.” A cat licking concrete could be an indicator of an underlying illness such as a vitamin or mineral deficiency, organ dysfunction, or a digestive problem, especially if it has developed suddenly. The only way to know if the behavior is a problem is to have your pet checked out by your vet. A complete physical exam, as well as bloodwork or other lab tests as indicated, will help to get to the bottom of this unusual behavior.
I hope this gives you a bit of guidance. Good luck!
Dr. Kim Hester