The origin of ultra-high energy cosmic rays (UHECRs) is an open question, but radio galaxies offer one of the best candidate acceleration sites. Acceleration at the termination shocks of relativistic jets is problematic because relativistic shocks are poor accelerators to high energy. Using hydrodynamic simulations and general physical arguments, I will show that shocks with non- or mildly relativistic shock velocities can be formed as plasma flows from the termination shock into the radio lobe and that these shocks have suitable characteristics for acceleration to 10-100EeV. I will discuss a model in which giant-lobed radio galaxies such as Centaurus A and Fornax A act as slowly-leaking UHECR reservoirs, with the UHECRs being accelerated during a more powerful past episode. I will also show that Centaurus A, Fornax A and other radio galaxies may explain the observed hotspots in the Auger and TA data at ultra-high energies.