We present results on the first principle study of the elastic constants and the phonon dispersion of EuFe2As2 at zero pressure. The ground-state energy calculations were performed within Density Functional Theory (DFT) and the generalized gradient approximation using the pseudopotential method with plane-wave basis sets. The projector augmented-wave (PAW) pseudopotentials were used in our calculation. The open source code QUANTUM ESPRESSSO was used with its pseudopotential database. The study on the elastic constants at zero pressure was a clear indication that the compound is mechanically stable, and the phonon dispersion study also indicated that the compound is dynamically stable. The elastic constants and mechanical properties also led to the conclusion that the compound is ductile and anisotropic.