A tolerance ring for applications requiring high axial static friction has contacting portions having a novel profile. The use of multiple contacting portions having a smaller size that are wedge-shaped increases rigidity and provides a directional grip that increases axial static function. Using multiple wedge-shaped contacting portions with appropriate opposite slants provides a balanced and symmetrical grip. Using inter-level wedge-shaped contacting portions with opposite slants provides a more aggressive grip while providing a tolerance ring that is more dynamically stable and has a high resonant frequency.