  A mechanism of ultra-high energy cosmic ray acceleration in extragalactic
radio sources, at the interface between the relativistic jet and the
surrounding medium, is discussed as a supplement to the shock acceleration in
`hot spots'. Due to crossing the tangential discontinuity of the velocity the
particle can gain an amount of energy comparable to the energy gain at the
shock crossing. However, the spectrum of particles accelerated at the jet side
boundary is expected to be much flatter than the one formed at the shock. Due
to this fact, particles accelerated at the boundary can dominate the overall
spectrum at highest energies. In conditions characteristic to extragalactic
jets' terminal shocks, the mechanism naturally provides the particles with E ~
10^20 eV and complies with the efficiency requirements. The spectrum formation
near the cut-off energy due to action of both the shock acceleration and the
tangential discontinuity acceleration is modelled with the Monte Carlo particle
simulations. It confirms that the upper energy limit can surpass the shock
acceleration estimate.
