Statistical　inferences　under　second　order　stochastic　dominance　for　two　sample　case　has　a　long　and　rich　history.　But　the　k(＞=　2)　sample　case　has　not　been　well　studied.　In　this　article　we　consider　k(＞=　2)　sample　test　for　the　equality　of　distribution　functions　against　second　order　stochastic　dominance　alternative.　A　test　statistic　is　constructed　with　isotonic　regression　estimates　of　stop-loss　transform　functions,　and　the　asymptotic　distribution　of　the　proposed　test　is　given.　A　bootstrap　procedure　is　employed　to　obtain　the　p-value　of　the　test,　and　some　simulation　results　are　presented　to　illustrate　the　proposed　test　method.