Recent measurements from the ATLAS experiment of the azimuthal anisotropy of charged hadron production in pp collisions at sqrt(s) = 2.76, 5.02 and 13 TeV and in p+Pb collisions at sqrt(sNN)= 5.02~TeV at the Large Hadron Collider (LHC) are presented. The measurements of the two-particle correlations using a template fitting procedure to remove correlations arising from hard-scattering processes are shown. The results on the per-trigger-particle yields, Y, as well as on vn Fourier coefficients are presented as a function of the charged particle multiplicity and transverse momentum for n = 2-4. Interestingly, v2 values in pp collisions are found to be approximately constant as a function of multiplicity. The pT-dependence of vn is similar to that measured in Pb+Pb collisions suggesting that in small systems features characteristic of the collective anisotropic flow are also present.