The lattice dynamics and elasticity of synthetic SrCO3 have been investigated by a combination of ab initio lattice dynamics calculations, microcalorimetry, Raman spectroscopy, X-ray thermal diffuse scattering and high-resolution inelastic X-ray scattering. The results of density functional based calculations were in all cases in good agreement with experiment. For the spectroscopic investigations, peak positions and intensities are well reproduced by the density functional theory model. Experimentally determined intensity distributions in thermal diffuse scattering maps differ from the theoretical distribution only in the (HK0) plane, a fact that is attributed to stacking disorder. As the model is accurate and reliable, the complete elastic stiffness tensor is predicted and, on the basis of these results, the anisotropy of the sound velocities is discussed, also in relation to the anisotropy in other carbonate systems.