Stress-measurement methods based on the overcoring method assume that the rock mass is linearly elastic, isotropic, continuous, and homogeneous. However, a rock mass is actually anisotropic to some degree. In this study, we carried out theoretical, numerical and experimental studies to apply the Downward Compact Conical-ended Borehole Overcoring technique to an orthotropic rock. Numerical experiments with the use of a 3D-FEM analysis were conducted to confirm the applicability and efficiency of the proposed measurement theory.The results showed that the measurement includes a non-negligible error if we do not consider the anisotropy of rock when such anisotropy is strong.For example, the isotropic assumption method gives an error of more than 20 % in the estimation of stress when the degree of anisotropy in the direction of the maximum applied stress exceeds 20 %. On the other hand, the error is less than 5 % in the orthotropic assumption method. Finally, laboratory experiments for four kinds of orthotropic rocks using a true-triaxial compressive apparatus were carried out to verify the efficiency of the proposed measurement theory. These experiments also verified that the proposed method is suitable for use in orthotropic rock.