This paper introduces a methodology for the direct determination of the shear moduli in transversely isotropic rocks, using a single test, where a cylindrical specimen is subjected to uniaxial compression. A method is also developed to determine the orientation of the isotropy plane as well as the dynamic elastic constants using ultrasonic measurements on a single cylindrical specimen. Explicit formulae are developed to calculate the shear moduli from strain gauge measurements at different polar angles. The calculation of shear moduli from these formulae requires no knowledge about Young's moduli or Poisson's ratios and depends only on the orientation of the isotropy plane. Several strain gauge setups are designed to obtain the shear moduli from different numbers and arrangements of strain gauges. We demonstrate, that the shear moduli can be determined accurately and efficiently with only three strain gauge measurements. The orientation of the isotropy plane is measured with different methods, including ultrasonic measurements. The results show, that the isotropy plane of the tested granitic samples slightly deviates from the foliation plane. However, the foliation plane can still determine the orientation of the isotropy plane with a good approximation.