In　this　paper,　we　consider　the　tau-relaxed　soft　capacitated　facility　location　problem　(tau-relaxed　SCFLP),　which　extends　several　well-known　facility　location　problems　like　the　squared　metric　soft　capacitated　facility　location　problem　(SMSCFLP),　soft　capacitated　facility　location　problem　(SCFLP),　squared　metric　facility　location　problem　and　uncapacitated　facility　location　problem.　In　the　tau-relaxed　SCFLP,　we　are　given　a　facility　set　F,　a　client　set　and　a　parameter　tau　＞=　1.　Every　facility　i　is　an　element　of　F　has　a　capacity　u(i)　and　an　opening　cost　f(i),　and　can　be　opened　multiple　times.　If　facility　i　is　opened　l　times,　this　facility　can　be　connected　by　at　most　lu(i)　clients　and　incurs　an　opening　cost　of　l　f(i).　Every　facility-client　pair　has　a　connection　cost.　Under　the　assumption　that　the　connection　costs　are　non-negative,　symmetric　and　satisfy　the　tau-relaxed　triangle　inequality,　we　wish　to　open　some　facilities　(once　or　multiple　times)　and　connect　every　client　to　an　opened　facility　without　violating　the　capacity　constraint　so　as　to　minimize　the　total　opening　costs　as　well　as　connection　costs.　As　our　main　contribution,　we　propose　a　primal-dual　based　(3　tau　+　1)-approximation　algorithm　for　the　tau-relaxed　SCFLP.　Furthermore,　our　algorithm　not　only　extends　the　applicability　of　the　primal-dual　technique　but　also　improves　the　previous　approximation　guarantee　for　the　SMSCFLP　from　11.18　+　epsilon　to　10.