Sputter fluxes in a bounded random medium are considered in comparison with the fluxes for an infinite-medium model. The basic equations connecting the two fluxes are derived and analyzed. It is shown that the fluxes in a bounded medium can be constructed if the infinite-medium ones are known. Analytical asymptotic formulas for the bounded-medium flux are found for the simplified case of factorized cross sections and self-bombardment. Explicit dependences of the asymptotic flux on incidence and exit angles, as well as energy variables, are calculated for the power cross sections and are compared with their infinite-medium counterparts. The results are generalized for a combination of two factorized scattering laws.