Permutation　and　multi-permutation　codes　have　been　widely　studied　due　to　their　potential　applications　in　communications　and　storage　systems,　especially　in　flash　memory.　In　this　paper,　we　consider　balanced　multi-permutation　codes　correcting　a　single　burst　of　stable　deletions　of　length　t　and　length　at　most　t,　respectively.　Based　on　the　properties　of　burst　stable　deletions　and　stabilizer　permutation　subgroups,　we　propose　two　constructions　of　multi-permutation　codes　correcting　a　single　burst　of　stable　deletions　of　length　up　to　some　parameter.　The　multi-permutation　codes　can　achieve　larger　rates　than　available　codes　while　maintaining　simple　interleaving　structures.　Moreover,　the　decoding　methods　are　given　in　proofs　and　verified　by　examples.