A previous two-step hydrodynamic model calculation of angle-resolved photoemission has been improved by modeling the surface with a soft analytic function. The same ground-state potential is used to screen the photon field and to calculate the electronic wave functions. The implemented code can be used for arbitrary ground state densities along the perpendicular direction. Mathematical and physical aspects of the model are discussed extensively. The behavior of the main peak of the spectrum in response to the variation of some parameters leads us to the conclusion that the peak cannot be interpreted as the direct excitation of multipole modes. This conclusion was suggested in the previous two-step model calculation.