  We have published the energy spectrum of ultra-high energy cosmic rays
(UHECRs) for E > 10^18.2 eV from our first 5-year observation with the surface
detectors of Telescope Array. We found two breaking points in the power-law
spectrum, a flattening known as the "ankle" or "dip" at E = 10^18.66 eV, and a
steepening at E = 10^19.72 eV. The spectral features must be related to
distribution of cosmic ray sources, injection spectrum, and energy loss
processes during propagation in inter-galactic space. We constructed a model of
source distribution of UHECRs and energy loss processes in the CMB photon field
to calculate energy spectrum to be observed at the Earth. The model includes
injection energy spectra at the sources, energy loss processes, and evolution
of cosmic ray fluxes with red shift. We consider two cases that the UHECR
sources are distributed uniformly, or same as galaxies in the local universe.
We found that the spectrum can be well fitted with the model. We discuss to
give a constraint to the model parameters, e.g. the injection power indices and
cosmological evolution from the observed data.
