This paper presents the development of an analytical method to determine the parameters of orientation and deformability of transversely isotropic cylinders of rock using the Council for Scientific Industrial Research (CSIR) triaxial cell under isotropic biaxial loading. The mathematical formulation is based upon the elastic and anisotropic constant transformation presented by Lekhnitskii (in: JJ. Brandstatter (Ed.), Theory of Elasticity of an Anisotropic Elastic Body, Holden-Day Series in Mathematical Physics, Holden Day Inc., San Francisco, 1963, 404p). By using three rosettes with four gages each, the method herein proposed permits the determination of the global tridimensional deformability characteristics of a rock cylinder, using only the local bidimensional deformation measurements provided by the rosette's gages. The new analytical method gives the direction and dip of the isotropy plane together with the magnitude of anisotropic elastic constants for transversely isotropic rocks of Class A (rocks with no visible symmetry planes) and Class B (with visible symmetry planes). No restrictions on the direction of the symmetry planes are imposed. This determination is obtained from strains measured in only one biaxial compression test performed with the CSIR cell on the overcore obtained from in situ stress test.