Abstract: The elliptic flow of prompt and non-prompt J/psi was measured in the dimuon decay channel in Pb+Pb collisions at root S-NN = 5.02 TeV with an integrated luminosity of 0.42 nb(-1) with the ATLAS detector at the LHC. The prompt and non-prompt signals are separated using a two-dimensional simultaneous fit of the invariant mass and pseudo-proper decay time of the dimuon system from the J/psi decay. The measurement is performed in the kinematic range of dimuon transverse momentum and rapidity 9 < p(T) < 30 GeV, vertical bar y vertical bar < 2, and 0-60% collision centrality. The elliptic flow coefficient, v(2), is evaluated relative to the event plane and the results are presented as a function of transverse momentum, rapidity and centrality. It is found that prompt and non-prompt J/psi mesons have non-zero elliptic flow. Prompt J/psi v(2 )decreases as a function of p(T), while for non-prompt J/psi it is, with limited statistical significance, consistent with a flat behaviour over the studied kinematic region. There is no observed dependence on rapidity or centrality.