X-ray burst sources represent a class of accreting neutron stars in close binary systems which do not exhibit any traces of the magnetic field. We present new method of hot model atmosphere computations with account of Compton scattering on free electrons and computed set of plane-parallel hydrogen-helium atmospheres and X-ray spectra of bursting neutron stars. Models were computed with precise angle-dependent radiative transfer under constrains of radiative and hydrostatic equilibrium. Compton scattering opacity included both the Klein-Nishina corrections and the effects of relativistic Maxwellian thermal motion of scattering electrons. Compton redistribution function allows for large energy exchange between X-ray photons and scattering electrons.