The Glasgow firm is building the wheels for the Bloodhound SuperSonic Car project and has now said it is manufacturing 18 solid aluminium wheels at the company's premises in Castlemilk.
Each wheel will have to spin 177 times per second if the target speed is to be achieved.
Family-owned Castle Precision Engineering is also supplying a number of other components including inner and outer wheel covers and inner wheel caps. Operations director Yan Tiefenbrun said: "Bloodhound is a huge technological and manufacturing challenge and an opportunity to be part of something very special.
"There are some 3000 parts that must be made for this project to work – but the fastest wheels in history will be made right here in Glasgow.
"It's a real point of pride and motivation in the company and a fantastic opportunity to showcase some of our capabilities."
The Bloodhound will be powered by a rocket attached to a Eurofighter-Typhoon jet engine and the attempt to break the land speed record, currently 760mph, is scheduled to take place in South Africa during November later this year.