The present invention describes a bio-medically compatible gripping device capable of radial collapse in accordance with the shrinkage of a nylon or other polymeric material cored surgical cable undergoing tension while maintaining a firm grip throughout the process. It provides a gripping device capable of maintaining a grip on the outer surface of a slippery delicate cable, the grip being approximately uniform along both the length and circumference of the cable. The present invention also provides a gripping device capable of maintaining a grip, yet not damage, a delicate cable under high tension for a period of time adequate for as the healing process to occur.