This paper presents a novel method to directly measure the out-of-plane shear modulus of transversely isotropic rocks by using a single cylindrical specimen subjected to uniaxial compression. This simple methodology relies on the measurement of strain at single or multiple points around the sample, and using those in an explicit formula to directly determine the shear modulus. In addition to the shear modulus, the plane of symmetry, the Young's moduli and the Poisson's ratio transverse to the plane of isotropy can be determined from this single test. Several experimental setups are proposed depending on whether the plane of symmetry is known or needs to be determined. Experimental results on three granitic samples show that the measured plane of symmetry is significantly deviated from the one apparent from the visual inspection of the foliation plane. In addition, the Saint-Venant formula is found to give an error of more than 10% for samples exhibiting a higher anisotropy ratio than 1.85.