The fact that so many in situ stress measurement techniques exist, may be a reflection of the need to adapt to the diversity of rock conditions encountered in nature, rather than a sign of inconsistencies in the methods. The determination of in situ stresses by direct measurement has received more attention as more engineers are conscious of the limitations and dangers encountered in empirical and “divinatory” approaches to ascertain in situ stresses. Knowledge of in situ stresses is not only one of the major prerequisites for the safe and efficient design of underground excavations such as mine openings, tunnels and nuclear waste repositories, but also a crucial requirement in the monitoring and rehabilitation of existing civil and mining engineering works. The results show the error on the estimated stresses is little affected by the scale at which the deformability parameters are determined and the main source of error is linked to the estimation of the stress component parallel to the borehole axis. The RPR method allowing calculating four far-field stress components from a single measurement had been developed for a homogeneous medium and is tested here for its effectiveness in heterogeneous materials. Using a numerical model, a two phase heterogeneous medium resembling concrete is modelled and the complete modified Doorstopper stress measurement operations, including stress relief drilling and recovered core reloading are simulated. By simulating stress measurements with the modified Doorstopper technique which can be applied to a variety of conditions including measurements in concrete structures, it is shown how heterogeneities found at the measurement scale can be accounted for and how the estimated stresses are influenced by heterogeneities found at different scales. As we know, rock, rock masses and concrete are not homogeneous and this will affect the accuracy of stress measurements. When using so-called overcoring techniques to estimate stresses in rock masses for site investigation or in concrete structures for monitoring purposes, stresses are derived from recovered strains using elastic stress–strain relationships for which the media is assumed to be homogeneous at all the scales involved in the measurement.