Starting from the condition of continuity of the traction vectors at a solid-liquid interface, with the aid of the field equations projected on the surface and with an iterative expansion procedure for the displacement field in the solid region adjacent to the interface we derived the equation describing the behaviour of a Newtonian fluid particle in contact with an elastic, solid surface. This equation relates the tangential velocity of the particle to the shear stress at the wall and to the second normal velocity gradient. The analysis shows that, while in the far field limit the no-slip condition holds, next to the contact line slippage is present which mainly depends upon the wall shear stress, upon the solid-liquid surface tension, and upon the elastic modulus of the solid surface.