Conceptualizing sophisticated measurement set-ups as well as testing and evaluation procedures for laboratory experiments on anisotropic rocks requires a basic understanding of the potential specimen behavior. The focus of the present work was therefore to investigate the influence of different transversely isotropic parameters and their ratios on the elastic behavior of cylindrical rock samples in uniaxial compression tests. Parameter sets corresponding to soft anisotropic rocks were chosen based on naturally observed ranges for the five elastic transversely isotropic constants. Analytical results for the radial and vertical strain distributions around the sample circumference and a comparison with finite element simulations are presented. Further, the effect of interface friction between samples and loading platens was analyzed within the numerical models. The results suggest that radial strains around cylindrical anisotropic samples are rarely uniform except for specific combinations of parameters and isotropy plane inclinations. The effect of interface friction was found to have a clear influence on the developing elastic stress and strain distributions for samples with inclined isotropy planes. Nevertheless, no significant influence of frictional boundary conditions on the back-calibrated values of the elastic parameters could be identified, suggesting that friction-reducing measures in uniaxial compression tests on transversely isotropic samples with predominantly linear behavior are not required.