Cerium 4f electrons are peculiar in being spatially localized with a radial extent much smaller than that of 5s and 5p semicore states, yet having an energy in the region of valence 6s and 5f electrons. Two phases, α and γ, of cerium are under debate in terms of different properties like elastic properties or phase transition properties. The mechanical and elastic properties of cerium have generated substantial interest over the years both experimentally and theoretically. Theoretical studies, concerned with the lattice dynamics, which may be of use, as it is expected from the electron-phonon interaction, and plays a significant role during the γ → α transition, are very limited.The aim of the present work is to study the behavior of lattice dynamics and elastic constants under increasing pressure using first-principles methods within linear response approach for the face-centered cubic (fcc) γ-cerium and shed some light on the interrelationship among the elasticity and phonons and understand the role of phonons in the phase transition. Our calculations reproduce zero pressure lattice dynamical and elastic properties of cerium with a very good precision.