In　this　paper,　we　investigate　the　free　sets　and　the　free　sub-semimodules　in　a　semimodule　over　a　commutative　semiring　S.　First,　we　discuss　some　properties　of　the　free　sets　and　give　a　sufficient　condition　for　a　nonempty　finite　set　to　be　free　in　a　finitely　generated　free　S-semimodule　and　obtain　a　relation　between　free　set　and　linear　independent　set　in　an　S-semimodule.　Then　we　consider　the　free　subsemimodules　and　prove　that　the　rank　of　any　free　subsemimodule　of　a　finitely　generated　S-semimodule　M　does　not　exceed　that　of　M.　Also,　we　give　some　equivalent　descriptions　for　a　commutative　semiring　S　to　have　the　property　that　all　nonzero　subsemimodules　of　any　finitely　generated　free　S-semimodule　are　free.　Partial　results　obtained　in　the　paper　develop　and　generalize　the　corresponding　results　for　modules　over　rings　and　linear　spaces　over　fields.　(C)　2016　Elsevier　Inc.　All　rights　reserved.