A mechanical model for a lubricated elastic half-plane weakened by surface and subsurface cracks is proposed. The interaction of an incompressible lubricant with elastic material within surface crack cavities is regarded as the most interesting aspect of the problem. Some necessary conditions characterizing the actual behavior of lubricant within crack cavities are proposed. They taking into account the pressure rise in closed cavities completely filled with lubricant and the possible onset of cavitation. The problem is reduced to a system of integro-differential equations with a number of additional conditions in the form of alternating equalities and inequalities. Due to the fact that the boundaries of crack cavities and the pressure in the cavities completely filled with lubricant are unknown, the problem is nonlinear. For the proposed formulation of the problem a new iterative numerical method is developed. The method is based on Gauss-Chebyshev quadratures and is different from the earlier used methods. It allows determination of crack faces' displacements and normal stresses acting on crack faces simultaneously. Besides, the method allows determination of the location of cavities fully/partially filled with lubricant and segments at which the crack faces are in contact with each other. This is crucial when a surface crack-lubrication interaction is considered. The method provides conservation of lubricant volumes trapped within the closed crack cavities. The method demonstrates fast convergence. In some instances the normal stress intensity factors for surface cracks are found to be several orders of magnitude greater than those for similar subsurface cracks.