“How do you stop partial dentures from moving?”

Depending on the age of the denture, it is not uncommon for the clasps to loosen and need tightening.  If your partial is made of cast metal, you should see your dentist and see if they can be tightened by crimping the clasps.  However, if your partial is beyond 7-8 year and older, it may be time for a new partial.  In the meantime, you can use denture adhesive and see if that can help.  Hope this helps, Dr. G. 

Sometimes, having a dentist perform a slight adjustment to the wire clasps will help. Most but usually the best but more expensive cure is using something like Dental Implants to hold it still.

You need to have them adjusted, and tightened up, by whoever made them for you.