Knowledge of the mechanical properties is of great clinical significance for diagnosis, prognosis and treatment of cancers. Recently, a new method based on Eshelby's theory to simultaneously assess Young's modulus (YM) and Poisson's ratio (PR) in tissues has been proposed. A significant limitation of this method is that accuracy of the reconstructed YM and PR is affected by the orientation/alignment of the tumor with the applied stress. In this paper, we propose a new method to reconstruct YM and PR in cancers that is invariant to the 3D orientation of the tumor with respect to the axis of applied stress. The novelty of the proposed method resides on the use of a tensor transformation to improve the robustness of Eshelby's theory and reconstruct YM and PR of tumors with high accuracy and in realistic experimental conditions. The method is validated using finite element simulations and controlled experiments using phantoms with known mechanical properties. The in vivo feasibility of the developed method is demonstrated in an orthotopic mouse model of breast cancer. Our results show that the proposed technique can estimate the YM and PR with overall accuracy of (97.06 ± 2.42) % under all tested tumor orientations. Animal experimental data demonstrate the potential of the proposed methodology in vivo. The proposed method can significantly expand the range of applicability of the Eshelby's theory to tumors and provide new means to accurately image and quantify mechanical parameters of cancers in clinical conditions.