Cubic solids such as NaCl, crystalline argon, or H 2 O-ice VII exhibit significant elastic anisotropy strongly increasing upon compression. As earlier recognized for solid argon and H 2 O-ice (both exhibiting Zener ratio A>1), longitudinal sound velocities of their polycrystals, V Lav , measured using Brillouin light scattering (BLS) or pulse-echo ultrasonics are much closer to V L111 than to V L100 , the V L-extremes in any cubic single crystal. Here, we experimentally confirm, using the technique of time-domain Brillouin scattering, the same tendency for NaCl exhibiting the opposite anisotropy type, A<1. To understand this tendency, we modelled orientational distribution and the frequency of occurrence of V L values in texture-free polycrystalline samples of NaCl and solid argon. We found a remarkable and predictable asymmetry of the V L distributions with maxima at V L110 which is always much closer to V L111. This asymmetry persists in BLS peaks but can be obscured in experiments. In the case of solid argon at 49 GPa, the asymmetry can lead to a moderate deviation of experimental V Lav from V LH (obtained from elastic-stiffness constants C ij applying the Hill approximation) by ~7%. The latter can cause, however, a significant overestimation of the aggregate shear modulus by δG/G~50% or of the bulk modulus by δB/B~20% if just one BLS peak of longitudinal modes is detectable. A similar analysis, performed for transverse sound velocities, V T and V Tav , has shown that, by use of a BLS spectrum showing peaks of both longitudinal and transverse modes, overestimation of B is similarly high but that of G is much less dramatic.