Structural properties of zinc oxide nanoparticles are theoretically studied focusing on the effects induced by the surfaces. In this aim, we compare two models: an atomistic and an elastic model. Atomistic model uses a semiempirical potential: the shell model. Effects of surface relaxation and surface stress are taken into account in this model while they were not in the elastic model. Studying nanoparticles with sizes varying from 1.5 to 4.5 nm, we show that surface relaxation occurs on a typical length of about 1 nm in the vicinity of surfaces within the atomistic model. This significant length is due to the existence of long-range interaction forces in zinc oxide which is an ionocovalent material. Because this typical length is comparable to nanoparticle size, elasticity fails to reproduce correctly structural properties of the nanoparticles. As an illustration of structural properties changes by decreasing nanoparticles sizes, we study the nanoparticles acoustic vibrations eigenfrequencies focusing on the mostly observable modes by vibration spectroscopy. Differences between elasticity and atomistic calculations are attributed to surface effects. If elasticity acceptably provides vibration frequencies of most studied nanoparticles, it fails to reproduce them for nanoparticles with a size below an approximate value of 2.5 nm. We expect such effects to be experimentally observable.