A new method for calculation of the diffraction elastic constants, based on the self-consistent model, is proposed and tested. This method is especially useful in the interpretation of the results of X-ray measurements since the ellipsoidal inclusion near the sample surface is considered. In X-ray diffraction the information volume of the sample is defined by absorption, causing unequal contribution of different crystallites to the intensity of the measured peak. Consequently, the surface grains participate more effectively in diffraction than the grains which are deeper in the sample.