•We present numerically evidence that the Poisson’s ratio is size dependent.•We show that the Poisson’s ratio varies with crystallographic orientation.•Materials display negative ratios at nanoscale despite positive at macroscale.•For small beams Poisson’s ratios are initially negative, but turn to positive.•Negative ratios exist at the nanoscale and values below −0.5 are possible. Elastic simulations of single-crystal copper nanobeams, of different cross section sizes and with crystallographic orientations 100 and 110 along their length directions, have been performed applying tensile mechanical loading. The molecular dynamics code LAMMPS was employed for the simulations. The Poisson’s ratio, which is one of the fundamental measures of the elastic deformation behavior of materials, has been determined. In this paper we present numerical evidence that the Poisson’s ratio of nanobeams loaded by finite strains varies with both size and crystallographic orientation. In particular, we provide numerical evidence for that, of the two Poisson’s ratio that naturally can be defined for nanobeams loaded in the 110-direction, one is negative whereas the other one remains almost constant, irrespective of applied strain. We also show that for nanobeams loaded in the 100-direction the values of Poisson’s ratio initially decrease, reaches a minimum and thereafter increase with applied strain. For the smallest 100 cross sections the Poisson’s ratios are initially negative, but turn positive at larger strains.