In order to study further the long-range correlations (“ridge”) observed recently in p+Pb collisions at $\sqrt{s_{NN}}$ = 5:02 TeV, the second-order azimuthal anisotropy parameter of charged particles, $v_2$, has been measured with the cumulant method using the ATLAS detector at the LHC. In a data sample corresponding to an integrated luminosity of approximately 1 microbarn-1, the parameter $v_2$ has been obtained using two- and four-particle cumulants over the pseudorapidity range |$\eta$| < 2.5. The results are presented as a function of transverse momentum and the event activity, defined in terms of the transverse energy summed over 3.1 < $\eta$ < 4.9 in the direction of the Pb beam. They show features characteristic of collective anisotropic flow, similar to that observed in Pb+Pb collisions. A comparison is made to results obtained using two-particle correlation methods, and to predictions from hydrodynamic models of p+Pb collisions. Despite the small transverse spatial extent of the p+Pb collision system, the large magnitude of $v_2$ and its similarity to hydrodynamic predictions provide additional evidence for the importance of final-state effects in p+Pb
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