Insights　into　the　reflection　and　transmission　(R/T)　of　waves　at　a　prestressed　interface　are　important　in　geophysical　applications,　such　as　evaluating　the　angle-dependent　elastic　properties　for　monitoring　geopressure　and　tectonic　stress　using　sonic　logging　data　or　seismic　data.　Although　many　studies　deal　with　wave　propagation　in　prestressed　media,　the　angle-dependent　R/T　of　waves　at　an　interface　subject　to　different　prestress　loading　modes　remains　largely　unaddressed.　We　address　this　issue　by　applying　the　theory　of　acoustoelasticity　with　third-order　acoustoelastic　constants　to　study　the　R/T　coefficients　at　the　interface　between　two　prestressed　media.　Stress-induced　elastic　deformations　are　assumed　to　be　locally　homogeneous　without　boundary　dislocations　caused　by　stress　concentration　so　that　the　static　boundary　conditions　can　be　applied.　We　consider　three　typical　prestress　modes　(confining,　uniaxial,　and　pure　shear),　each　of　which　takes　into　account　the　incidence　of　upgoing　and　downgoing　P　and　S　waves.　The　Knott　equations　under　different　types　of　prestresses　are　derived,　followed　by　the　estimation　of　angle-dependent　R/T　coefficients.　The　energy　conservation　at　the　interface　and　the　acoustoelastic　finite-difference　simulation　of　predicted　P　and　S　modes　verify　the　correctness　of　the　angle-dependent　R/T　coefficients　under　confining　prestress.　Comparisons　with　the　elastic　case　(prestress　σ=0　MPa)　indicate　the　important　influence　of　prestresses　on　the　energy　distribution　of　reflected　and　transmitted　waves,　including　stress-dependent　critical　angles,　converted　waves,　and　R/T　energy　ratios.　Such　acoustoelastic　effects　mainly　occur　around/after　the　critical　angle.　For　small-angle　incidence,　prestresses　mainly　affect　the　gradient　of　R/T　coefficients.　The　type　and　magnitude　of　prestress　are　closely　related　to　the　angle-dependent　R/T　coefficients　and　must　be　considered　for　amplitude-variation-with-offset　analysis　in　prestressed　media.　　©　2024　Society　of　Exploration　Geophysicists.