Acoustic phonon dispersion has been measured in the cubic phase of NaBH4 by the inelastic x-ray scattering (IXS) technique using single crystals of natural isotope composition at room temperature. Experimental results are compared with the compressibility data and the previously published ab initio calculations. Comparison of the elastic properties derived from the diffraction and IXS experiments indicates a non-negligible contribution (below 10%) of nonhydrostatic effects in the diffraction experiments. Strong preferred orientation in the compressed samples is also revealed by Rietveld analysis of the synchrotron powder-diffraction data.