  Three-dimensional hydrodynamic simulations of large scale structure in the
Universe have shown that accretion shocks form during the gravitational
collapse of one-dimensional caustics, and that clusters of galaxies formed at
intersections of the caustics are surrounded by these accretion shocks.
Estimated speed and curvature radius of the shocks are 1000-3000 \kms and about
5 Mpc, respectively, in the $\Omega=1$ CDM universe. Assuming that energetic
protons are accelerated by these accretion shocks via the first-order Fermi
process and modeling particle transport around the shocks through Bohm
diffusion, we suggest that protons can be accelerated up to the {\it Greisen
cutoff energy} near $6\times 10^{19}$ eV, provided the mean magnetic field
strength in the region around the shocks is at least of order a microgauss. We
have also estimated the proton flux at earth from the Virgo cluster. Assuming a
few (1-10) \% of the ram pressure of the infalling matter would be transferred
to the cosmic-rays, the estimated flux for $ E \sim 10^{19}$eV is consistent
with observations, so that such clusters could be plausible sources of the UHE
CRs.
