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The origin of ultra-high energy cosmic rays (UHECRs) has been an openquestion for decades. Here, we use a combination of hydrodynamic simulationsand general physical arguments to demonstrate that UHECRs can in principle beproduced by diffusive shock acceleration (DSA) in shocks in the backflowingmaterial of radio galaxy lobes. These shocks occur after the jet material haspassed through the relativistic termination shock. Recently, several authorshave demonstrated that highly relativistic shocks are not effective inaccelerating UHECRs. The shocks in our proposed model have a range ofnon-relativistic or mildly relativistic shock velocities more conducive toUHECR acceleration, with shock sizes in the range 1-10kpc. Approximately 10% ofthe jet's energy flux is focused through a shock in the backflow of $M>3$.Although the shock velocities can be low enough that acceleration to highenergy via DSA is still efficient, they are also high enough for the Hillasenergy to approach $10^{19-20}$eV, particularly for heavier CR composition andin cases where fluid elements pass through multiple shocks. We discuss some ofthe more general considerations for acceleration of particles to ultra-highenergy with reference to giant-lobed radio galaxies such as Centaurus A andFornax A, a class of sources which may be responsible for the observedanisotropies from UHECR observatories.

Ultra-high energy cosmic rays from shocks in the lobes of powerful radio galaxies