Problems connected with determination of stress distribution in sliding layer of thin-walled bearing bushes, investigated in bearing fatigue test rigs, have been presented. Using an example of plain bearings tested in the fatigue machine SMOK (built at the Gdańsk University of Technology) problems with obtaining a convergence of iterative procedure for determining the fatigue strength estimators of bearing alloy surface layer are analyzed. Calculations consisting in successive iterations of pressure distribution in oil film and corresponding elastic deformation of the bearing bush and housing were based on finite-element method and utilized ANSYS program. The objective of calculation was the estimation of values of radial, tangential, axial and reduced stresses in surface layer of the bearing bush corresponding to experimentally determined load magnitudes leading to fatigue cracks initiation. The convergence of analytical procedure has been achieved by the use of a relaxation method.