One of the most popular techniques applied to measure residual stresses is the hole-drilling technique. The technique is easy to be applied at industry, and is normalized ASTM E 837. However, due to the stress concentration caused by the machined hole, the technique can not be used if the residual stresses are higher than one third of the material yield strength, Sy. There are several researches articles that evaluate the errors aroused from the use of linear-elastic coefficients in case where plastic strains are present. In general, those articles apply the finite element to simulate the process of drilling the hole and stress relief. In certain case it is showed that the error can reach 140% of the applied stress. However,those articles use linear-elastics hypothesis and therefore their predictions can also include mistakes. The present work proposes new numerical methodologies to evaluate the usefulness of the hole- drilling technique, as it is described by the ASTM E 387, in the plastic range. The aim is to model the stress relief caused by the hole`s drilling process in a more realistic way, in order to avoid the use of linear-elastics hypothesis. The proposed methodologies are: Equivalent State, in which is applied in the hole a stress equivalent to that one acting externally on the component; Element Death, in which the drilling process is simulated by eliminating numerically in several steps the material which vanishes during the drilling process, and the Replacement Stress; in which the material in the hole is replaced by the stress that is acting at its walls. Those mentioned methodologies were implemented using a commercial finite element program which simulated plates with through the thickness and blind holes. Those plates have been loaded with three different loadings which varied from 0.3 to 0.9 Sy. Two materials with different stress-strain curves have been used. One of them had the elastic limit equal to the yield limit and the other one has those two limits different. In the worst case the errors found were 70 percent, which is smaller than those found by others researchers. It was concluded that, the Replacement Stress and the Elements Death methodologies are those that best simulate the process of drilling a hole in a plate which is under high stresses.