L. A. Galin was probably the first who has considered the contact problem for a half-space with an additional concentrated force applied outside the contact area [1]. <...> A similar contact problem for a two-layered elastic base was investigated earlier [2] without additional force. <...> The Galanov’s method used below to take the additional concentrated force into account allows us to estimate the influence of the extra force onto the contact pressure as well as onto the force applied of the punch. <...> This problem is of interest for the contact mechanics of the bodies with coverings. <...> Consider the contact problem of the indentation of a punch into an elastic layer of the thickness The shape of the punch foot is described by the function and half-space are 1, ν1 and of an elliptic paraboloid, i. e. <...> The elastic characteristics of the layer 2, ν2, respectively. <...> To solve the contact problem and equation (1) we use the method of nonlinear boundary integral equations based on the theorems discussed in [2, 3]. <...> Let the contact area be a priori included into the rectangle , , , 2 1 , 2 2 , To calculate the function integral 0 The elastic materials chosen for calculations and their elastic parameters (Young's modulus son's ratio ν) are presented in Table 1. <...> The shear modulus is given by formula Modulus Material Carbon steel Cold-drawn brass Concrete Elastic parameters 10–4 (MPa) 20 9 2 2 1 ν ν 0.28 0.35 0.17 The two following cases were taken for the calculations: steel on brass (case A) and steel on concrete (case B). <...> The dimensionless parameter λ characterizes the relative thickness of the elastic layer. ( ) in formula (2) one should extract its principal term by using the , . 2 1 κ 2 , θ 1 ν Here, Ω is an unknown contact area. <...> As the force contact area), the force and the pressure increases and also as the value of and the pressure will drop because of the force 0 are greater than those and the pressure drop because the top steel layer decreases (the force goes to the input becomes significant. <...> The obtained results have a clear mechanical sense helping us to estimate the extra force influence onto the typical contact characteristics. <...> The Galanov’s method is quite effective for the threedimensional elastic contact analysis <...>