  Elastic photon-photon scattering can only occur via loop diagrams in the
standard model and is naturally suppressed. Unparticle can induce tree-level
photon-photon scattering through the operator F_{\mu\nu} F^{\mu\nu} O_\U for
spin-0 unparticle or F_{\mu\alpha} F^{\alpha}_{\nu} O^{\mu\nu}_\U for spin-2
unparticle. Due to the peculiar CP-conserving phase \exp(-i d_\U \pi)
associated with the s-channel unparticle propagator, its interference effects
with the t- and u-channels on the total cross section and the angular
distribution are found to be some significance. In addition, we show that the
cross sections via unparticle exchange can be substantially larger than the
standard model contribution.
