The three - dimensional Galin’s type contact problem for a two - layered elastic base (a layer completely attached t o a half - space from another material) is investigated when an extra loading (concentrated force) is applied o utside the contact area. The contact zone is supposed to be unknown. The punch foot form is an elliptic parabol oid. The pro blem is reduced to an in tegral equation with respect to the unknown contact pressure distributed in the unknown contact zone. Galanov’s method of nonlinear boundary integral equations is used to determine the con tact pressure and the contact zone simultaneously. Calculations made for various values of elastic and geometric parameters a llow estimating an extra force input to the dependence between the punch settlement and the force app lied to the punch. The problem is important for the strength analysis of coated surfaces of variou s elastic solids subjected to contact and extra loadings. The solution can be also useful in the frame of the discrete contact the ory for bodies with rough surfaces.