Contact of an elastic ball stamp and a titanium cylinder with a ceramic coating based on zirconium dioxide is considered. It is shown that at contact interaction tensile stresses occur in the coating, which can lead to cracking of the coating. The dependencies of the intensity of these stresses on the elastic properties of the spherical stamp, stamp radius and the yield strength of titanium are examined. It is shown that nano-titanium due to its high yield strength is preferable at the local impacts, as compared to conventional coarse-grained titanium for such designs.