In this paper, laser texturing is performed on the surface of Mn-Cu and Fe-Zn damping alloys and the tribological properties of the samples with various surface weaves under dry-sliding conditions are investigated. The results show that the surface weave parameters affect the size of the contact surface and change the number of micro-convex bodies at the contact interface. This leads to changes in the tangential damping of the contact and further affects the magnitude of the friction coefficient. Additionally, the damping properties significantly affect the wear mechanism and make it more prone to adhesive wear.