An algorithm of the layer growing/removing method is presented for computing residual stresses in case of the thin inhomogeneous circular disc with a central hole, from strain measurements on the free stationary contour or from X-ray diffraction measurements on the disc's moving contour. The algorithm is valid for layer growing/removing on the outer or inner contour of the disc and is of interest first of all in the study of residual stresses in coatings and surface layers generally. The suggested algorithm is programmed for PC. Two examples of application are presented.