The　scattering　and　diffraction　of　waves　by　irregular　surface　profiles　is　of　interest　in　seismology　and　in　many　other　areas.　Diverse　techniques　have　been　proposed　to　quantitatively　study　the　problem.　Among　them,　domain　approaches　such　as　finite　differences,　spectral　elements　and　finite　elements　have　been　used.　Because　the　reduction　of　dimensionality　boundary　formulations　is　widely　used.　Recently,　the　direct　boundary-element　method　has　been　applied　using　some　series　approximations　for　surface　scattering,　including　the　preconditioned　splitting　series,　for　the　numerical　description　of　rough　surface　scattering.　Extending　further　and　simplifying　this　approach,　we　use　the　indirect　boundary-element　method.　The　ensuing　Fredholm　integral　equation　of　the　second　kind　that　arises　in　IBEM　leads　to　a　very　efficient　iterative　scheme　based　on　the　classical　Jacobi　method.　A　discussion　of　direct　and　indirect　approaches　is　presented.　Assuming　incident　SH　waves,　results　are　obtained　with　the　various　approaches　and　compared　among　them　for　both　a　canyon　and　a　hill,　both　of　semicircular　shape.　Besides,　an　example　is　presented　of　a　surface　profile　that　produces　strong　scattering.　This　was　inspired　by　the　diverse　problems　that　arise　in　the　emerging　field　of　metamaterials.　©　Seismological　Society　of　America.