The　stability　of　trenches　for　buried　submarine　pipelines　(TBSPs)　during　excavation　and/or　prior　to　backfilling　has　not　received　enough　attention　in　the　literature.　In　this　study,　the　undrained　stability　of　TBSPs　in　horizontal　and　inclined　seabeds　with　shear　strengths　increasing　linearly　with　depth　is　investigated　using　the　lower　and　upper　bound　finite　element　limit　analysis　(FELA).　The　surcharge　due　to　excavated　soils　and　trenching　machines　is　reasonably　considered.　Extensive　parametric　studies　are　performed　on　the　trench　slope　angle　β,　normalized　width　of　trenching　machine　L/H,　dimensionless　strength　gradient　Hk/su0　and　the　volume　ratio　R　(for　inclined　seabed　only)　of　the　excavated　soil　stacked　on　the　upside　and　downside　of　trenches.　The　actual　results　are　accurately　bracketed　by　the　computed　upper　and　lower　bound　solutions.　For　the　trench　with　horizontal　seabeds,　the　maximum　stability　can　be　obtained　under　β　=　70°–80°.　For　inclined　seabeds,　the　global　stability　of　TBSPs　roughly　reaches　peak　value　for　different　combinations　of　L/H　and　β　when　R　=　0.15–0.3.　©　2019,　©　2019　Informa　UK　Limited,　trading　as　Taylor　&　Francis　Group.