We　consider　the　facility　location　problem　with　submodular　penalty　(FLPSP)　and　the　facility　location　problem　with　linear　penalty　(FLPLP),　two　extensions　of　the　classical　facility　location　problem　(FLP).　First,　we　introduce　a　general　algorithmic　framework　for　a　class　of　covering　problems　with　submodular　penalty,　extending　the　recent　result　of　Geunes　et　al.　[11]　with　linear　penalty.　This　framework　leverages　existing　approximation　results　for　the　original　covering　problems　to　obtain　corresponding　results　for　their　submodular　penalty　counterparts.　Specifically,　any　LP-based　α-approximation　for　the　original　covering　problem　can　be　leveraged　to　obtain　an-approximation　algorithm　for　the　counterpart　with　submodular　penalty.　Consequently,　any　LP-based　approximation　algorithm　for　the　classical　FLP　(as　a　covering　problem)　can　yield,　via　this　framework,　an　approximation　algorithm　for　the　submodular　penalty　counterpart.　Second,　by　exploiting　some　special　properties　of　FLP,　we　present　an　LP　rounding　algorithm　which　has　the　currently　best　2-approximation　ratio　over　the　previously　best　2.50　by　Hayrapetyan　et　al.　[13]　for　the　FLPSP　and　another　LP　rounding　algorithm　which　has　the　currently　best　1.5148-approximation　ratio　over　the　previously　best　1.853　by　Xu　and　Xu　[27]　for　the　FLPLP,　respectively.　©　2013　Springer-Verlag　Berlin　Heidelberg.