The contact interaction of a punch with an elastic half-plane under the action of a symmetrical normal load is considered. Inside, the flat horizontal base of the punch is perfectly connected to the border of the half-plane, and at the edges it is peeled away from the border with the formation of cracks, the edges of which are in a state of frictional sliding. The considered problem is a generalization of the well-known Galin problem on contact with adhesion and sliding of a punch and an elastic half-plane. Using the Wiener-Hopf method, the integral equation of the problem is reduced to an infinite system of algebraic equations. The contact stress distributions and shear stress intensity factor are found.