<p>In the present paper, we study the role of gradient in the material properties of contacting bodies in the difference between static and kinetic friction for a Hertzian geometry, according to the theory of "Griffith friction", for which the transition from stick to slip occurs as an elastic instability. We use the term "Griffith friction" to suggest an energy balance approach in mode II to derive stable and unstable equilibrium configurations, where in particular macroscopic sliding can occur by a global elastic instability, analogous to a Griffith crack which doesn’t arrest after reaching a critical size. The most important conclusion are that static friction coefficient: (i) is increased with harder surface; (ii) is increased for small normal loads and tends to infinity in the limit of zero load. These conclusions hold both in the case of a constant frictional fracture energy or a pressure-dependent frictional fracture energy at the interface.</p>